Large efforts have been devoted in the past to understanding size effect in shear failures of members without transverse reinforcement. Experimental works have demonstrated that increasing the size reduces the nominal shear strength provided that the failure mode is brittle. For large specimen sizes where a linear behavior can be assumed between the opening of the shear cracks and the acting shear force, the size effect agrees with linear-elastic fracture mechanics (LEFM). In this case, the reduction of nominal shear strength is characterized with respect to the specimen size by an asymptotic slope (in double-log scale) of -1/2. However, such a linear relationship between crack widths and applied shear force is not present in most reinforced concrete structures, where the response is characterized by a nonlinear behavior at a cracked stage. In these cases, the influence of size effect shall be milder, and the slope (in double-log scale) characterizing it shall be lower than -1/2. In this paper, the influence of size effect on structures characterized by internal redundancy (continuous one-way members and slabs in case of punching shear with a nonlinear response) is investigated in the frame of the critical shear crack theory. The theory predicts the same influence as LEFM with respect to size effect when a linear behavior can be assumed, but it yields consistently milder influence of size effect for structurally redundant elements with a nonlinear response.