A complete set of nonlinear equations and associated boundary conditions for a piezoelectric waveguide layer in a vacuum is proposed for the purpose of studying both bulk and surface nonlinear phenomena of electroacoustic wave propagation. The electro elasticity equations in a piezoelectric and in a non-material medium (in a vacuum) are derived in their invariant (material) form considering geometric nonlinearity. They are based on the strict use of nonlinear continuum mechanics and electrodynamics of a non-material medium with electromechanical interrelations. The propagation of finite-amplitude electroelastic shear waves in a piezoelectric layer of class 6mm hexagonal symmetry considering only geometric nonlinearity is considered. It is shown that the propagation of an electroactive shear linear signal in adjacent non-material regions induces a coupled electromagnetic elastic wave field, and the primary signal in the piezoelectric layer is strongly distorted. The distortion measures of the wave components of the electroelastic field in the first approximation by numerical analysis are investigated.