Bioresorbable thermoset elastomers and methods of making the same are disclosed. In certain embodiments, the thermoset elastomers include soft segments comprising branched polyesters, and hard segments including urethane and/or urea. The thermoset elastomers are made in certain embodiments by curing a branched prepolymer with a cross-linking agent. In certain embodiments, the mechanical properties of the thermoset elastomers are tailored by selecting the average molecular weight of the prepolymer, or by tuning the ratio of prepolymer to the cross-linking agent during curing, or by selecting a cross-linking agent with specific chemical characteristics.