According to the current codes and guidelines, shear assessment of existing reinforced concrete slab bridges sometimes leads to the conclusion that the bridge under consideration has insufficient shear capacity. The calculated shear capacity, however, does not consider the transverse redistribution capacity of slabs, and thus leads to overly conservative values. While mechanics-based models have attempted to describe the problem of one-way shear in concrete slabs under concentrated loads, this problem is still not fully understood. Therefore, this paper proposes an artificial neural network (ANN)-based formula to come up with estimates of the shear capacity of one-way reinforced concrete slabs under a concentrated load that are as good as possible based on 287 test results obtained from the literature. The methods used for this purpose are: (i) the development of the database with experimental results from the literature, and (ii) the development of the ANN-based matrix formulation. For the latter purpose, many thousands of ANN models were generated, based on 475 distinct combinations of fifteen typical ANN features. The proposed “optimal” model yields maximum and mean relative errors of 0.0% for the 287 datapoints. Moreover, it was illustrated to clearly outperform (mean Vtest / VANN = 1.00) the Eurocode 2 provisions (mean VE,EC / VR,c = 1.59) for that dataset. A step-by-step assessment scheme for reinforced concrete slab bridges by means of the ANN-based model is also proposed in this work, which results in an improvement of the current assessment procedures.