A nonlinear analysis procedure for steel-concrete (SC) composite structures is presented. The procedure uses smeared crack concrete constitutive modeling done on the basis of the disturbed stress field model and supplemental material models that are used to incorporate response contributions of the steel faceplates comprising SC composite elements. The procedure is implemented within the framework of a thick-shell finite-element analysis program and is verified using experimental data pertaining to SC composite structural elements subjected to exclusively in-plane or exclusively out-of-plane (i.e., through-thickness) loading conditions. Lastly, the shell structure analysis program is used to numerically investigate the performance of SC composite elements subjected to combined in-plane and out-of-plane shear forces, an area directly relevant to SC infrastructure applications, yet one that is limited in the existing database of literature.