Membrane flexoelectricity is an electromechanical coupling process that describes membrane bending and membrane electrical polarization caused by bending under electric fields. In this paper we propose, formulate, and characterize a stress-sensor device for mechanically loaded solids, consisting of a soft flexoelectric thin membrane attached to the loaded deformed solid. Because the curvature of the deformed solid is transferred to the attached flexoelectric membrane, the electromechanical transduction of the latter produces a charge that is proportional to the stress of the solid. The model of the stress-sensor device is based on the integration of the thermodynamics of polarizable membranes with isotropic solid elasticity, leading to a transfer function that identifies the elastic, electromechanical, and geometrical parameters involved in electrical-signal generation. The model is applied to representative normal bending and then to more complex off-axis bending of elastic bars. In all cases, a common transfer function shows the generic material and its geometric contributions. The sensor sensitivity increases linearly with flexoelectricity and the membrane–solid interface, and the sensitivity decreases with increasing membrane thickness and Young′s modulus of the solid. The theoretical results contribute to ongoing experimental efforts towards the development of anisotropic soft-matter-based stress-sensor devices through solid–membrane interactions and electromechanical transduction.