Reinforced concrete bridge deck slabs make up a significant portion of bridges worldwide and are designed to efficiently withstand traffic loads. The empirical design method, specified in the Canadian Highway Bridge Design Code (CHBDC), uses the inherent arching action in these slabs to provide strength and durability. The PUNCH program was developed to analyze externally restrained steel-free bridge deck slabs, but it cannot analyze directly deck slabs with embedded reinforcement. This research focuses on modifying the PUNCH program to enable the analysis of internally reinforced deck slabs by introducing the concept of equivalent diameter for embedded reinforcement. The study investigates how the axial stiffness of steel-concrete composites changes under varying loads and integrates these findings into the modified program, PUNCHED. The enhanced program accounts for equivalent diameters to accurately model reinforced concrete deck slabs under different loading conditions. Validation using experimental data from multiple studies confirms that PUNCHED reliably predicts both load-deflection behavior and ultimate failure loads. The findings demonstrate that the modified PUNCHED program provides a dependable tool for engineers to evaluate the performance of reinforced concrete deck slabs. By bridging the gap between empirical design and analytical modeling, this research contributes to more precise and effective analysis of bridge deck slabs.