Redistribution of shear forces in reinforced concrete members without shear reinforcement is a key aspect for the assessment of the shear capacity of wide beams and slabs. Such redistributions are due to the nonlinear response of reinforced concrete (both in bending and shear) and have the potential to significantly modify the internal forces during loading. This phenomenon allows in many cases, as for slabs linearly supported and subjected to concentrated forces, to increase the level of load even when some regions have already attained their local shear resistance. This work introduces the results of an experimental programme performed on three cantilever slabs subjected either to strip loads or to concentrated loads. Shear redistributions close to failure are investigated on the basis of refined measurements performed on the concrete surface and on the reinforcement bars. The results show the significance of several mechanical parameters, as well as how shear redistributions occur when some regions are in softening (post-peak behavior) while others have still not attained their local shear resistance. On this basis, a comprehensive approach is presented for determining the redistributions of internal forces and to predict the shear capacity of reinforced concrete slabs subjected to concentrated loads near linear supports. The performance of such approach is eventually validated against test data and practical recommendations are proposed for design and assessment.