A finite element model based on solid-like shell elements is presented for the simulation of progressive damage in laminated composite structures. To model mesh independent matrix cracking, a discontinuous solid-like shell element (DSLS) is utilized. The shell element has only displacement degrees of freedom, thus avoids the need for a complicated update of rotation degrees of freedom in nonlinear applications. To model delamination phenomena, a shell interface model is presented. The model allows computationally efficient simulation of delamination. To model the coupled response of matrix cracking and delamination under large deformations, a computational framework is developed. The combined modeling of matrix cracking and delamination is achieved without incorporation of additional degrees of freedom. In addition to physical nonlinearities, the numerical model is also able to simulate geometrical nonlinearities. Numerical examples are presented to simulate failure resulting in cracking and delamination in laminated composites.