Low density shape memory polymer foams hold significant interest in the biomaterials community for their potential use in minimally invasive embolic biomedical applications. The unique shape memory behavior of these foams allows them to be compressed to a miniaturized form, which can be delivered to an anatomical site via a transcatheter process, and thereafter actuated to embolize the desired area. Previous work in this field has described the use of a highly covalently crosslinked polymer structure for maintaining excellent mechanical and shape memory properties at the application-specific ultra low densities. This work is aimed at further expanding the utility of these biomaterials, as implantable low density shape memory polymer foams, by introducing controlled biodegradability. A highly covalently crosslinked network structure was maintained by use of low molecular weight, symmetrical and polyfunctional hydroxyl monomers such as Polycaprolactone triol (PCL-t, Mn 900 g), N,N,N0,N0-Tetrakis (hydroxypropyl) ethylenediamine (HPED), and Tris (2-hydroxyethyl) amine (TEA). Control over the degradation rate of the materials was achieved by changing the concentration of the degradable PCL-t monomer, and by varying the material hydrophobicity. These porous SMP materials exhibit a uniform cell morphology and excellent shape recovery, along with controllable actuation temperature and degradation rate. We believe that they form a new class of low density biodegradable SMP scaffolds that can potentially be used as “smart” non-permanent implants in multiple minimally invasive biomedical applications.