In this work, layerwise SAM-L model for thin to moderately thick laminated shells is introduced. Generalized equations are obtained from a stress approximation and from Hellinger–Reissner functional (Reissner, 1950). Stress approximation verifies the 3D equilibrium equations and boundary conditions on shell faces. Hellinger–Reissner functional allows identifying 5 generalized displacements per layer. The equations of the model are obtained using Reissner’s variational principle. The model takes into account in its constitutive equations the Poisson’s effect of out-of-plane normal stresses on in-plane strains. To prove the accuracy of the model, SAM-L is applied to the analysis of laminated cylinders and one catenoid. SAM-L results are compared to exact solutions, solid finite elements, and other models available in the literature. SAM-L shows high quality in predicting the stress and displacement fields, even for thick shells. Edge effects on interlaminar stresses are assessed with high precision. SAM-L model proves to be an alternative to solid finite elements and other higher computing cost theories for structural analysis of doubly curved laminated shells.