Slabs subjected to concentrated loads close to supports, as occurring for truck loads on slab bridges, are less studied than beams in shear or slab-column connections in punching. To predict the shear capacity for this case, the Bond Model for concentric punching shear was studied initially. Modifications to this model resulted in the Modified Bond Model, which takes into account the enhanced capacity from the direct transfer of the load to the support, is able to deal with moment sign changes as occurring near continuous supports, and can take into account the reduction in capacity, resulting from the geometry when the load is placed close to the edge. The model is then compared to the results of experiments on slabs subjected to concentrated loads close to supports. As compared to the Eurocode and the ACI code, the Modified Bond Model leads to a significantly better prediction of the experimental results. The Modified Bond Model is one of the few models available to describe the shear capacity of slabs subjected to concentrated loads close to supports and can be used for design and assessment.