Abstract: A method for extruding foam of a thermoplastic elastomer, which is a blend of olefin rubber and polyolefin resin, includes the steps of mixing the thermoplastic with water, introducing the mix to an extruder, melting and compressing the thermoplastic elastomer and water and extruding the resultant mix as foam. In more detail, a first quantity of thermoplastic elastomer in pellet form is mixed with a second quantity of water. The mixed water and thermoplastic elastomer is introduced to an extruder. The thermoplastic elastomer is allowed to soak for a predetermined period of time after mixing. The thermoplastic elastomer is melted and mixed with the water to a uniform mix of thermoplastic elastomer and water. The mix is extruded through a die, wherein the water expands in a vapor form to create foam cells with the cells having walls of the thermoplastic elastomer.