The objective of this work is to provide a reliable numerical model using the finite element method for the analysis of steel–concrete composite beams for short-time loads. For this purpose, a computer program was developed in this study. The reinforced concrete (RC) slab is modeled using degenerated curved shell elements based on Mindlin theory, while plane shell elements based on Kirchhoff theory were used for modeling the steel beam. Stud shear connectors were modeled using 3D beam elements with special characteristics to take into account partial interaction at the slab–beam interface. Within the theory of plasticity, properly yield functions were considered for the concrete slab and the steel beam. A nonlinear elastic law proved to be adequate for treating the tangential forces in the stud shear connectors. Finally, some typical numerical examples of steel shells, RC plates and steel–concrete composite beams found in the literature are reproduced with the present numerical model and the obtained results are compared with the experimental data. The present numerical model is able to reproduce the path failure, collapse loads and failure mechanism with an acceptable level of accuracy.