I was trying to figure out a way to do something with my old or torn tires that I no longer use. So much work goes into the engineering, design, and production for these high quality rubber tires it would be a shame to just throw them away. I found that a machine screw set or some rivets can go a pretty far way with old bike tires. Since the rubber is usually of high quality, bike tire rubber is durable, flexible and a good base material to make other stuff.
In this case, I needed a basket on my bike rack to carry my back pack around and the flexible nature of the tires allow my back back to fit tight and have an adjustable size to accomodate small to large objects to haul.

Step 1: Tools & Material

You'll need the following tools:
1) Drill & drill bit
2) Screw driver
3) Sheet metal cutters
4) Wire cutters
5) Clamp
6) Tape measure
7) Rivet gun

You'll need the following materials:
1) Old tires
2) Lots of short machine screws, washers, & nuts. Most hardware stores sale kits which I would recommend as I always need machine screws.
2) Bicycle Rack and Bicycle
3) 1/4" & 1/2" rivets if you use a rivet gun

Step 2: Cut the Old Tires to Size

Make the old tires into strips
Use the wire cutters to cut the outer bead of the tire as this is usually made out of steel wire or kevlar. After cutting the bead, you can cut ther rubber with the sheet metal cutters. Of all the siccors out there, I found sheet metal cutters are best at cutting rubber so far.

You can either choose to rip the tire and keep only the flat part so the basket will be flexible or use the entire tire. I found that the outer beads keep the tire rigid so I used the entire width of the tire for the vertical pieces. For the upper part that required a little more flex, I cut off the beads of the tire and ripped the tire to be the width of a belt. This helps to fit the belt buckle I used to fasten the upper strap.

Step 3: Layout the Tires Around Your Basket

1) Figure out the general height that you want your basket. (I used 9")
2) Measure the overlap required around the rack and around the top band of the basket. (I used 1 1/2" for both the top and bottom)
3) Cut the tires to necessary size. (I cut my pieces to ~11")

Step 4: Machine Screws or Riveting Tires Around the Rack

Drill holes where necessary to fasten the rubber together around the rail of the rack. I used a screw gun to make the hole for the machine screw/rivet. If you use rivets, I would suggest using a washer on the back side of the rivet to help hold the rubber in. I used a mixtures of aluminum rivets and stainless steel rivets juse because that's what I hade. My machine screws are zinc which are not advisable due to the corrosion. See pictures for more information.

Note: Machine screws and rivets are interchangeable.

Step 5: Fasten the Top Band Around the Front Side of the Basket

I used a smaller flexible piece of rubber ripped from the center of a really old 25C road tire. It works well to expand and flex to what you need to put in your basket. I fastened the top band similar to the bottom and bent the vertical pieces over the top and sandwiched the top band. If you're using rivets, make sure you're rivet will be long enough to thread through the stack of rubber. Washers will be necessary. Hold off on fastening the back vertical post as you'll have to make this piece into a sleeve to allow the top band for expanding and contracting the basket.

Step 6: Belt Loop the Back Vertical Piece

On the back piece (connected to the end of the bike rack), make sure you give enough room for the top band to move freely through to allow expansion and contraction of the basket. Make sure you have enough slack on the top band also. If not, you'll just have to splice in more rubber at the end.

Step 7: Install Belt Buckle

I found an old belt buckle from my college days and rarely use it anymore. Install the belt buckle to the top band of the basket near the back. make sure the clamp on the back side of the belt buckle is shut down tight. Test the belt buckle to make sure you can tighten and loosen without destroying the rubber or compromising your load.

Ride around and test out the basket. To avoid the basket from wobbling around too much when it's not carrying a load. I carry around a binder clip to secure everything down.