Because it is porous and flexible, foam rubber can be particularly tricky to glue. However, the flexibility and versatility of this material make it a popular product to use in costumes, craft projects and kid's rooms. Although gluing foam rubber is not impossible, using the right product will help ensure success. The strongest adhesives are sold mostly for commercial applications in large quantities, but you can be achieve the desired result with consumer versions as well.
An easy-to-use adhesive for many foam rubber projects, spray glue is available from various manufacturers. Because different formulations of spray adhesives are made for different purposes, be sure the product is made for permanent bonding. You can buy spray adhesives at craft and discount stores, but commercial products are stronger. Look for 3M's Fastbond or similar products for a long-lasting hold.
Cyanoacrylates - Super Glue
Another type of glue that works well for adhering foam rubber is glue containing cyanoacrylate, more commonly known as Super Glue. Some spray adhesives may contain cyanoacrylates as well. These chemicals are known as instant glues, because they do not require other products to activate them coupled with their ability to cure quickly. You can buy the glues under many brand names, but for foam gluing, avoid the cheaply made varieties. Buy a cyanoacrylate glue made for foam, such as Permabond, Foam Tac, CraftFoam Glue or Loxeal 32.
Silicone is a versatile bonding and sealing material used for many purposes. Some formulations of silicone glue do work well for bonding silicone rubber. You can purchase silicone in bulk at a hardware or home improvement store, or look for specialty name brands for specific purposes such as the Goop line of glues.
Craft tacky glues will work for some foam rubber applications. They do not work well, however, with open cell foams that are porous and absorbent, given the fact that this type of glue soaks into the foam and doesn't stick. For closed-cell foam rubber, such as craft foam, tacky glue is a good solution. Keep in mind that it has to be used in rather thin coats and must cure for an extended period of time, unlike instant glues that bond in a few seconds.