This paper presents the results of numerical investigations into the behavior of a sinusoidal web loaded in shear due to buckling in the period from the onset of buckling until failure, as well as the impact of a reinforced concrete slab on the stability of the web. The analysis concerned steel girders and composite girders with the top flange bonded to a reinforced concrete slab. Nonlinear analyses were performed using the finite element method. The results of the investigations support the conclusion that the appearance and propagation of shear stresses in the sinusoidal web of the composite steel–concrete beam are the same as those in an identical non-composite steel beam, but the bracing of the top flanges improves the shear strength and, at the same time, affects the location of initial stresses. In addition, it was found that, despite the three types of buckling, the predominant failure of the sinusoidal webs, regardless of the presence of the concrete slab, is global buckling. It occurs diagonally through several folds at the same time, including deformation of the web over its entire height.