This paper utilizes data-driven approaches, namely Nonlinear Regression and Genetic Programming, to predict the capacity at the onset of diagonal cracking and at shear failure for prestressed concrete bridge girders. Shear failure is catastrophic in concrete beams, and thus, it is crucial to have sufficient shear capacity to prevent such failures. However, while numerous shear design models have been developed, there are still significant differences between experimental data and strength limits provided by the various models adopted in shear provisions within design standards worldwide. To overcome this issue, recent advancements in machine learning models have been utilized as an alternative to identify potential relationships and estimate the shear capacity associated with both the onset of diagonal cracking and ultimate shear failure. This research investigates Nonlinear Regression and Genetic Programming through a dataset of 882 specimens from 87 historical experiments carried out between 1954 and 2020 as a means of formulating a shear capacity equation that can provide accurate estimates of the shear resistance at the onset of shear cracking and at shear failure. Overall, the models produced from these methodologies estimate more accurately the experimental response as compared to the nominal shear strength equations in the ACI 318-19 and the 2020 AASHTO LRFD Bridge Design Specifications, which are intended for design, as opposed to prediction, and thus provide conservative estimates of the shear capacity. In comparison, the developed expressions provide predictions that are more accurate, i.e. closer to the experimental data, and more precise, i.e. have lower dispersion, compared to the strength equations available in design codes.