When a multilayer elastomeric bearing is sheared by end loads, the top and bottom surfaces of a typical plate are subjected to a shear stress distribution which causes bending of the plate. A new approach to the analysis of these bearings is presented which systematically takes into account the flexibility and subsequent warping of the plates. First, the displacement field of the bearing and the shear stress distribution are derived, within the framework of classical linear elasticity, from compatibility conditions between rubber pad and steel plate. Next, use of a second-order approximation to the nonlinear equilibrium equations leads to a new expression for the critical load of the bearing which depends on the bending stiffness of the plate. Under the assumption of perfectly rigid plates, this expression is in agreement with previous formulations. For flexible plates, however, the proposed expression shows that previous formulations lead to an overestimate of the buckling load which might become important for extremely thin plates and low values of the shear modulus of the rubber.