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, thus leading to overconservative values. 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, based on 287 test results gathered from the literature. The proposed model yields maximum and mean relative errors of 0.0% for the 287 data points. Moreover, it was illustrated to clearly outperform (mean V_test / V_ANN =1.00) the Eurocode 2 provisions (mean V_E,EC / V_R,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, which results in an improvement of the current assessment procedures.