An inelastic material model for laminated composite plates and shells is formulated and incorporated into a finite element model that accounts for both geometric nonlinearity and transverse shear stresses. The elasto-plastic material behavior is incorporated using the flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropic parameters of plasticity are introduced with isotropic strain hardening. The shear deformation is accounted for using an extension of the Sanders shell theory and the geometric nonlinearity is considered in the sense of the von Karman strains. A doubly curved isoparametric rectangular element is used to model the shell equations. The layered element approach is adopted for the treatment of plastic behavior through the thickness. A wide range of numerical examples is presented for both static and dynamic analysis to demonstrate the validity and efficiency of the present approach. The results for combined nonlinearity are also presented. The results for isotropic results are in good agreement with those available in the literature. The variety of results presented here based on realistic material properties of more commonly used advanced laminated composite plates and shells should serve as references for future investigations.