The present work deals with a generalization of geometrically linear shear deformation theory for multilayered anisotropic shells of general shape. No assumptions are made other than to neglect the transverse normal strain. The results, which include the effects of shear deformations and rotary inertia as well as initial curvature (included in the stress resultants and assumed transverse shear stresses) are deduced by application of the virtual work principle, with displacements and transverse shear as independent variables. These equations are applied to different shell geometries, such as revolution, cylindrical, spherical and conical shells as well as rectangular and circular plates.