Shape memory properties of two thermoplastic multiblock copolymers composed of poly(lactic acid) (PLA) and poly(ethylene glycol) (PEG) having different PEG‐segment lengths of 6 and 11 kDa were studied. The performance as a shape memory polymer at high strain level (600%) and its interrelations with shape‐programming conditions, molecular orientation, and microstructural changes are elucidated. A significant contribution of strain‐induced crystallization of PLA segments to the improvement of temporary shape fixation was evidenced upon increasing draw ratio and/or shape‐holding duration as well as programming temperature (within certain range) without largely sacrificing the shape recoverability. Series of microstructural characterizations reveal the occurrence of fibrillar‐to‐lamellar transformation upon shape recovery (at 60 °C) of the samples programmed at 40 °C, generating shish–kebab crystalline morphology. Such phenomenon is responsible for the high‐strain shape memory effect of these materials. The unprecedented formation of shish–kebab structure at such relatively low temperature (instead of the melting temperature range) in solid state observed in these copolymers as well as their high‐strain shape memory functionality would bestow the promising future for their practicability in diverse areas. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 241–256