A two-dimensional theory is presented for the analysis of deep, doubly curved, multilayered shells, The theory is based on a kinematical approach in which the continuity conditions for displacements and shear stresses at layer interfaces and on the bounding surfaces of the shell are exactly satisfied. It also takes into account refinements of the shear and membrane terms, by means of trigonometric functions as proposed previously for the transverse shear. The accuracy of the proposed theory is assessed through investigation of significant problems for which an exact three-dimensional elasticity solution is known: first, the bending of a three-layered, laminated, symmetric cross-ply rectangular plate, simply supported along all edges, submitted to a double sinusoidal transverse loading, and second, the bending of a circular, cylindrical panel. Results obtained with the model are compared with those yielded by previous theories. The sensitivity of the model to edge effects, for a hard-clamped, free-edge cylindrical panel, is also examined.