The new combinations of monomers presented in this work were evaluated in order to create an elastic material for potential application in soft tissue engineering. Thermoplastic elastomers (TPE) of trimethylene carbonate (TMC) with L-lactide (LLA) and 1,5-dioxepan-2-one (DXO) have been synthesized using a cyclic five-membered tin alkoxide initiator. The block copolymers were designed in such a way that poly(trimethylene carbonate-co1,5-dioxepan-2-one) formed an amorphous middle block and the poly(L-lactide) (PLLA) formed semicrystalline terminal blocks. The amorphous middle block consisted of relatively randomly distributed TMC and DXO monomer units, and the defined block structure of the PLLA terminal segments was confirmed by C-13 NMR. The properties of the TMC-DXO-LLA copolymers were compared with those of triblock copolymers based either on LLA-TMC or on LLA-DXO. Differential scanning calorimetry and dynamic mechanical analysis data confirmed the micro-phase separation in the copolymers. The mechanical properties of the copolymers were evaluated using tensile testing and cycling loading. All of the copolymers synthesized showed a highly elastic behavior. The properties of copolymers could be tailored by altering the proportions of the different monomers.