Provided is a melt composition for a heat shrinkable foam structure that includes at least one base polymer and a blowing agent made from at least one heat-activated chemical compound encapsulated by a plurality of polymeric shells. The melt composition may also include a crosslinking promoter or other additives. Also provided is a method for making a heat-shrinkable polymer foam tubing. A melt composition containing at least one base polymer material having a melt temperature and a blowing agent having an activation temperature is provided. The melt composition is mixed at an elevated temperature. The melt composition is then extruded through a die at a high temperature. The extruded foam tube is then processed, often heat-processed. Additionally provided is a heat shrinkable foamed polymer tube containing an inner layer and an outer layer of an extruded foamed polymer tube, where each layer is made from at least one base polymer and a blowing agent and the blowing agent includes a heat-activated chemical compound encapsulated in a plurality of polymer shells.