Abstract The present study introduces a rigorous higher-order polynomial in the thickness coordinate to develop a theory with thickness and shear deformations for doubly curved, laminated composite shells. In this theory, the nonlinear terms in all the kinematic parameters are kept. By applying the conditions of zero transverse normal and shear stresses at the top and bottom surfaces of shells, a third-order thickness and shear deformation theory with six kinematic parameters is derived. This is a particularly interesting result since the developed theory presents a single additional parameter to describe the thickness deformation with respect to the popular Reddy’s third-order shear deformation theory, which has five parameters. The accuracy of the proposed six-parameter theory is tested for static and dynamic benchmark cases. Results are also very satisfactorily compared to those obtained with a more sophisticated and computationally onerous nine-parameter theory. The considered cases are isotropic and cross-ply laminated circular cylindrical shells under radial forces and pressure, and nonlinear forced vibrations of a cross-ply laminated shell under harmonic radial excitation.