Biodegradable shape memory elastomers have the potential for use in soft tissue engineering, drug delivery, and device fabrication applications. Unfortunately, few materials are able to meet the targeted degradation and mechanical properties needed for long-term implantable devices. In order to overcome these limitations, we have designed and synthesized a series of unsaturated polyurethanes that are elastic, degradable, and nontoxic to cells in vitro . The polymerization included a nucleophilic thiol-yne Michael addition between a urethane-based dipropiolate and a dithiol to yield an α,β-unsaturated carbonyl moiety along the polymer backbone. The alkene stereochemistry of the materials was tuned between 32 and 82% cis content using a combination of an organic base and solvent polarity, which collectively direct the nucleophilic addition. The bulk properties such as tensile strength, modulus, and glass transition temperature can also be tuned broadly, and the hydrogen bonding imparted by the urethane moiety allows for these materials to elicit cyclic shape memory behavior. We also demonstrated that the in vitro degradation properties are highly dependent on the alkene stereochemistry.