Poly(ether block amide) (PEBA) thermoplastic elastomers are used in many different applications, with recent development being on those which show promise as high gas flux membranes. PEBA copolymers with high polyether soft block content are possible candidates for gas separation applications due to their high permeability relative to current commercially used polymers and good selectivity for acid gases such as CO2. To be effective and efficient, the high flux must be maintained over the course of production and use. A series of PEBA copolymers containing poly(tetramethylene oxide) and polyamide-12 was studied to explore the influence of mechanical orientation and copolymer composition on gas permeability and morphology. Upon uniaxial orientation, several compositions of PEBA copolymers exhibited a significant decrease in permeability, both in the oriented and elastically recovered states. Copolymer composition strongly influenced the degree of change seen in the permeability upon orientation. WAXS and DSC were used to identify strain-induced crystallization that occurred during orientation. Rubbery materials can crystallize under high strains, and PEBA is no exception. Strain-induced crystallization of the polyether blocks produced a tortuous path for gas diffusion, resulting in as much as a 3.5× decrease in permeability for oriented PEBA films. To maintain high flux for membrane applications, elastic recovery and thermal treatment proved beneficial in reversing the effects of uniaxial orientation on PEBA copolymers.