In this paper, to deal with complex damage propagations in various composite structures under quasi-static transverse loads, a numerical simulation methodology based on the three-dimensional (3D) finite element method (FEM) is proposed. In this numerical model, two categories of damage patterns existing in composite structures under transverse loads are tackled independently. First, a kind of stress-based criteria is adopted to deal with the first category, which includes various in-plane damages, such as fiber breakage, transverse matrix cracking, matrix crushing, etc. Second, a bi-linear cohesive interface model is employed to deal with the second category, i.e., interface damages, such as delaminations. Also, to overcome the numerical instability problem when using the cohesive model, a simple and useful technique is proposed. In this technique, the move-limit in the cohesive zone is built up to restrict the displacement increments of nodes in the cohesive zone of laminates after delaminations occurred. The effectiveness of this method is illustrated using a DCB example and its characteristic is discussed in detail. This numerical model is further applied to various composite structures, such as 2D laminated plates and 3D laminated shells under transverse loads. The results of the numerical simulations are compared with the experimental results and good agreements are observed. The obtained information is helpful for understanding the propagation mechanisms of various damages in composite structures.