The punching shear resistance of reinforced concrete flat plates is an area where design is typically done in a highly-idealized manner, using provisions developed from experimental results of isolated slab-column connections; yet, involves structures where performance may be greatly impacted by system-level response. This paper presents the development and application of a practical thick-shell finite element-based nonlinear modelling procedure for reinforced concrete flat plate slab systems. Cracked concrete material modelling based on the formulations of the Disturbed Stress Field Model is employed in conjunction with computationally-efficient layered thick-shell finite elements that accommodate through-thickness shearing effects and are shown to be capable of capturing brittle punching-governed failure modes. A simple low-cost sectional analysis modification procedure is proposed to incorporate strength enhancements attributed to confining effects stemming from disturbances in slab-column connection regions. Load-displacement responses and failure modes developed using the proposed modelling procedure are shown to capture observed experimental responses and provide response estimates similar to those obtained using more costly three-dimensional solid continuum finite element modelling techniques. Finally, the analysis results presented were developed using simple-to-define concrete property input without the need for supplemental material model or analysis parameter calibration.