Smectic‐A liquid single crystal elastomers (SA‐LSCE) are materials where the rubber elasticity of the polymer network is combined with the one‐dimensional positional long‐range order of mesogenic groups which are covalently attached to the network. In the systems investigated so far, a mechanical deformation of the network causes significant reorientation processes of the layered structure. We present a new type of SA‐LSCE in which this structure remains unaffected on mechanical deformation both parallel and perpendicular to the director. The thermoelastic behavior, macroscopic dimensions, and stress–strain measurements parallel as well as perpendicular to the director are investigated. X‐ray studies confirm that a deformation parallel and perpendicular to the layer normal does not alter the macroscopically ordered lamellar structure with respect to the order parameter and the layer correlation length. We propose a simple picture where defects within the lamellar structure might account for these findings.magnified image