The shear strength evaluation of reinforced concrete bridge deck slabs by accurate models can indicate strength reserves and avoid costly operations necessary for the extension of their lifetime. This article introduces an approach that extends the Critical Shear Displacement Theory model (CSDT) for reaching higher levels of approximation of the shear strength for slabs subjected to concentrated loads close to the support. A database with 141 tests of wide reinforced concrete members under concentrated loads close to the support failing in one-way shear was built. The tests represented typical loads in bridge slabs and were assessed through a combination of CSDT with different models of effective shear width. In other analyses, the entire database with 214 test results of slabs failing by different mechanisms was evaluated and a general effective shear width model was proposed (GESW). The best results, which are a function of the effective shear width model used, reached a mean ratio between experimental and predicted shear capacities of 1.06 with a coefficient of variation of 14%, which is similar to that reported by some studies including linear and non-linear finite element analyses. Furthermore, this level of accuracy was insensitive to the shear slenderness and support conditions of the tests. The extended CSDT predicted the shear capacity of bridge deck slabs in preliminary analyses more precise than semi-empirical models provided in the current design codes, and the level of accuracy is comparable to methods using Linear Elastic Finite Element Analyses (LEFEA). Moreover, our proposed combination of the CSDT with a general effective shear width model (GESW) provides reasonable levels of accuracy for slabs under concentrated loads regardless of the failure mode of the tests. Therefore, the proposed approaches can be applied to bridge deck slabs, which are subjected to a variety of loading and support conditions.