Nonlinear finite-element analyses are used to numerically investigate the punching shear resistance of reinforced concrete flat plate structures. Material nonlinearity is based principally on the formulations of the disturbed stress field model, a smeared crack reinforced concrete modeling procedure. Low-cost three-dimensional solid finite elements and one-dimensional truss bar finite elements are used to represent concrete and steel reinforcement, respectively. Requiring only easily defined concrete material properties and employing fundamental finite-element meshing techniques, the modeling approach was found to provide good response estimates for slab–column connection assembly tests under concentric shear loading conditions and was shown to effectively capture the effects of design parameters on slab punching shear performance: reinforcement ratio, column size, and slab thickness. The validated modeling approach was used to perform a brief numerical investigation on the effects of boundary conditions on the punching shear capacity of multibay flat plates. The results from the investigation were compared to the response obtained for an equivalent isolated slab–column assembly specimen and to existing code provisions and two-way shear analysis procedures.