Those are both pretty. Here's several ideas for you.

For the left one, fill the vase with something like marbles, clear would work great. Then put in a single peony. Trim it so the flower sits down on the top and the stem touches the bottom of the vase. For daisy like flowers play around with just a few standing up in the middle in a bunch with the stems all the same length. Florists will even use a stem tied around the bunch to keep them in place.

It's a modern style vase that calls for a simple arrangement. Try stacking them in rows by color from short to long, front to back. Instead of marbles you can also use small limes, cranberries or beads. Anything pretty to hold the flowers in place.

The same idea should work for the one on the right. Keep flowers in the dips around the edge short and use marbles to hold them. The middle should be higher. Try a linear arrangement to fit the shape of the vase.

You could use scotch tape to create a grid.

Tape from side to side and back to front, leaving openings large enough to poke stems through.

When you are done with the tape, cut through the middle and pull off towards the side, instead of trying to pick the ends off the vase. :)

Like the two previous posters, having support to hold the stems more upright instead of using the vase sides will help. In addition to their ideas, I have also seen a glass insert with holes to put stems in that is placed in the bottom of the vase. Also, not for these vases since they have see-through sides, but if you have ceramic vases there is floral foam and an old-fashioned device called a frog, basically a metal piece with lots of tall spikes to anchor the flowers.

Everyone above is right. You need what flower arrangers call "mechanics". You can try their suggestions or you can buy some needle-type frogs to put in the bottom of the vases.

Most garden clubs have a few, or many, members who love flower arrangers. If you have a GC in your town, ask if you could stop over to find out the best type of mechanic for your vases. I bet they'd love a question like that.

All arrangers keep lots of different types of mechanics for their amazing displays. A good arranger would enjoy helping with the challenge of your vases, making beautiful arrangements while still showing off those unusual openings.

Those are tough vases! Gotta get pretty creative with those.

I just made my first flower arrangements for competition, and learned that a kenzan is a great tool for clear glass vases. It's also known as a metal pin frog. Your modern-looking vase would look great with a big leaf, an iris or two, and a nasturtium leaf at the front. You can look up Ikebana to see how to arrange with very few flowers for a modern looking vase like that.

The other vase would look great with fanned out arrangements. You could put a line of five fern fronds across the back, with two hanging down. Then your daisies fanned out in front of them, slightly lower. Longer daisies could hang out on the sides, with the ferns beneath them.

I think you might enjoy the modern vase with just greenery in it too. When I run out of flowers, that's what I do.
Renee

Here is a link that might be useful: kenzan

Here's my first try, and though I have a long way to go this is 1000% percent better than any previous attempts! I did have some glass flower arranging marbles I had gotten for a school craft earlier, and using those and I ribbon I got the flowers to at least stand up. It's a start!

Renee, I'll look up the Ikebana stuff, and thanks for the link to the frog. I'm having a hard time visualizing an arrangement with "a" nasturtium leaf at the front. That is really zen!

Next we'll try the suggestions for the fan vase. It will be so nice to be actually able to use these vases. Thanks for all the suggestions!

Looks good, that's a great start. Nice to see you figured out the written instructions. Thanks for posting this. Those flowers are beautiful, love that you used all one color since the vase calls for a simple arrangement.

I'm really looking forward to seeing the other vase arranged too.

Another tip for you. Once you get comfortable with this method, cut the front flowers shorter than the back and try tilting them forward a bit so they fill up the vase opening a little more.

Tip noted!

I hoped the monocolor would agree with posters suggestions of simplicity and modernity, so I appreciate your confirmation. The other one will be harder to figure out and I don't have much in my flower garden right now that I can see in a fan arrangement. Will take more thought.

Ruds are so easy. Cut 'em, stick 'em in an old mayonnaise jar, and they look great!

You can always use foliage plants without flowers. Use odd numbers like five stems and fan them out. If you have plants with interesting woody stems, you can use those too.

Those vases would look awesome with just a single giant hosta leaf or other similar plant leaf.

Roses cut to sit right on the top would work too.

Hi Deanna-
I love to arrange flowers although my sister is the real star in the family. I agree-you need structure-here are a couple of ideas:

buy wet foam (comes in green blocks, Wal Mart or Michaels carries it), cut it to fit bottom of vase (abut 4 inches) and then you can poke all the stems in it to stabilize the arrangement. To hide the block cover the inside of the vase with leaves (layering on the outside of vase) or fill the outside with gravel or rocks.

gather vines (I use my virginia creeper, wisteria or ivy) and I wind them around and put them in the bottom of the vase. Now you have something to stick the flower stems in.

another trick is to get a smaller vase (or jar) and put it in the large vase then hide it by pouring rocks etc around it.

The Barefoot Contessa says to make the bouquet in your hand and then put it in the vase.

Hope this helps! Those are some beautiful vases.

Instead of the ribbon to support the arrangement, do you have shrubbery with full branches (such as boxwood or similar)? You can snip off very short branches and arrange under the flowers in front and use longer ones for behind and sides. I've used boxwood and it outlasts the flowers. But you can experiment with other branches of greenery, tucking them around.

Criss cross stems of greenery (remove all leaves that will be below the water line) to make a grid. Then add your flowers continuing to weave them in. Add the heaviest stems last.

Nice. Here's another style. Do what some in the art of Ikebana do.. Visualize a triangle. Have a tall stem and a middle stem and a low stem. The taller stem can be an interesting twig like a harry lauder's walking stick. The middle a flower and the lower stem a bunch of flowers spilling over.

Instead of marbles you can use black polished river stones.

Invisible tape to use as a grid on top will help with stabilizing the stems on top.

Thanks again for the continuing suggestions. ianna, Harry Louder's Walking Stick is probably my favorite woody plant. One day i will have one, but that day will be later because of the price tag. What an eye-catching plant!

buyorsell888, at first I couldn't visualize your idea, but now I think I get it. At first I was thinking you meant criss-cross horizontally, as in parallel to the floor, with greenery. Now I'm thinking you mean put the greenery in the vase first, criss-crossing the stems to sit diagonally to make a support for the flowers. That's a good idea!

teakettle, I like the vase-in-a-vase idea!

OOh Deanna, you can plant a harry Lauder walking stick in your garden. I have this plant and it's spectacular. It does well in my zone. Anyway, you can so substitions of course. This was just an example of putting together a scenery.