A procedure for nonlinear analysis of RC slabs and shell structures is presented. Cracked RC is treated as an orthotropic material governed by a smeared rotating crack procedure and the constitutive formulations of the disturbed stress field model. The analysis procedure is implemented within the framework of a finite-element program employing layered thick-shell elements that consider out-of-plane (through-thickness) shear deformations. A simple modification method employing an effective shear strain concept is introduced to improve the out-of-plane performance of the layered shell element for RC applications. The adequacy of the procedure is verified using test data of RC members controlled by out-of-plane shear failure mechanisms and elements under combined in-plane and out-of-plane loading scenarios. The nonlinear finite-element program is shown to be suitable for elements exhibiting ductile or brittle responses, and the shear modification method introduced is found to be capable of capturing out-of-plane shear failures.