Biodegradable and biocompatible elastomers are highly desirable for many biomedical applications. Here, we report synthesis and characterization of poly(ε-caprolactone)-co-poly(β-methyl-δ-valerolactone)-co-poly(ε-caprolactone) (PCL-PβMδVL-PCL) elastomers. These materials have strain to failure values greater than 1000%. Tensile set measurements according to an ASTM standard revealed a 98.24% strain recovery 10 min after the force was removed and complete strain recovery 40 min after the force was removed. The PβMδVL midblock is amorphous with a glass-transition temperature of -51 °C, and PCL end blocks are semicrystalline and have a melting temperature in the range of 52-55 °C. Due to their thermoplastic nature and the low melting temperature, these elastomers can be readily processed by printing, extrusion, or hot-pressing at 60 °C. Lysozyme, a model bioactive agent, was incorporated into a PCL-PβMδVL-PCL elastomer through melt blending in an extruder, and the blend was further hot-pressed into films; both processing steps were performed at 60 °C. No loss of lysozyme bioactivity was observed. PCL-PβMδVL-PCL elastomers are as cytocompatible as tissue culture polystyrene in supporting cell viability and cell growth, and they are degradable in aqueous environments through hydrolysis. The degradable, cytocompatible, elastomeric, and thermoplastic properties of PCL-PβMδVL-PCL polymers collectively render them potentially valuable for many applications in the biomedical field, such as medical devices and tissue engineering scaffolds.