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The provisions for punching shear around concentrated loads in the new Model Code 2010 (MC2010) have been updated, covering a large number of design cases such as slabs with and without transverse reinforcement, different column/slab geometries and prestressed slabs amongst others. The theoretical framework used was based on the mechanical model of the Critical Shear Crack Theory (CSCT). This approach, in contrast to empirical formulas, provides the designer with a physical understanding of the phenomenon and allows an enhanced flexibility to implement new parameters, which may arise in practice when introducing innovative structural solutions to increase the punching strength. This paper summarizes the basis for the derivation of the design formulas introduced in the new Model Code 2010 and shows a comparison with test data from the literature including tests carried out at École Polytechnique Fédérale de Lausanne. Several levels of approximation are presented depending on the complexity of the method used to estimate the slab rotations. Lastly, it is shown that approximated formulas and shear fields can be used for particular and general cases consistently with the CSCT