Abstract The empirical design of reinforced concrete bridge deck slabs of girder bridges, referred to as only ‘deck slabs,’ is the most efficient design method because it recognizes the inherent arching action that exists in these slabs. Because of the arching action, the deck slabs fail in a punching shear mode under much higher wheel loads than the loads that would make them fail in bending; it is noted that failure in bending assumes the absence of the arching action. The Canadian Highway Bridge Design Code provides specifications for the empirical design of deck slabs. As the term ‘empirical design’ implies, this method is based on experimental evidence rather than analytical methods. A computer program, PUNCH, based on an analytical method, was developed to analyze the failure loads of externally restrained deck slabs, also referred to as ‘steel-free deck slabs,’ which do not contain embedded reinforcement for strength. In this program, it is assumed that the transverse confinement to deck slabs is provided by steel straps lying outside the deck slabs. Thus, this program only models the behavior of externally reinforced bridge deck slabs accurately. For internally reinforced bridge deck slabs, the stress-deformation behavior of steel in concrete is investigated in experimental evidence on concrete prisms, each with an embedded central steel bar, which has confirmed that when these prisms are subjected to tensile forces through the steel bars, the axial stiffness of the composite prisms is initially much larger than that of the bare steel bar, and decreases nonlinearly with the increase in the magnitude of tensile force. A reinforced concrete prism can thus be conceptually replaced by a hypothetical equivalent steel bar, the diameter of which is larger than that of the bare steel bar and decreases with the increase in the magnitude of the tensile force. This thesis attempts to modify the program PUNCH to analyze deck slabs with embedded steel bars by replacing the bars with hypothetical equivalent steel bars that lie outside the concrete. The first part of the research work involves the establishment of the changing equivalent diameter of the composite concrete prisms under gradually increasing tensile forces. This research was conducted through non-linear finite element analysis, the results of which were compared favorably with available experimental results. The second part of the research was first to modify the PUNCH program to include variable axial stiffness of the external restraint and then to use the modified program to analyze a large number of deck slabs with variable external stiffness represented by hypothetical steel bars of varying equivalent diameters. The accuracy of the results has been established by comparing its results with those from available experimental tests, some of which were failure tests. Predictions from the modified PUNCH have confirmed that most reinforced concrete deck slabs never fail under wheel loads of even the heaviest commercial trucks traveling on highways. The modified PUNCH program is now called PUNCH.ED, can be used with confidence for predicting not only the failure loads of deck slabs but also their load-deflection behavior under smaller; loads.