Size effect has been theoretically and experimentally acknowledged as a phenomenon influencing the shear and punching shear strength of concrete structures, with reducing unitary shear strength for increasing member sizes. For members failing in shear, as beams or one-way slabs without transverse reinforcement subjected to uniform loading, size effect has shown to have a variable influence, with low significance for failures governed by limit analysis (strength or yield criterion) and large influence for members failing in a brittle manner. When the response of a member failing in shear can be reasonably approximated by a linear behaviour (i.e. linear relationship between the acting shear force and the crack widths), the predictions of Linear Elastic Fracture Mechanics (LEFM) can be applied to asymptotically large specimen sizes. This phenomenon can for instance be demonstrated by the Critical Shear Crack Theory (CSCT) and leads to a dependence of the shear strength with the power -1/2 of the size of the specimen. Nevertheless, in actual structures failing in shear (as slabs or shells), the structural response is normally characterized by some level of redundancy and capacity to redistribute internal forces in the longitudinal and transversal directions. In this case, the relationship between the acting shear force and the crack widths is not linear (with lower crack widths associated to larger shear strengths) and the influence of size effect on the shear strength is milder than that predicted by LEFM. With respect to punching (shear failures due to concentrated loads in two-way slabs), a similar behaviour is observed with respect to size effect. A low dependency can be observed when limit analysis governs whereas, for brittle failures, size effect becomes significant. In this case, it can be observed that the behaviour of slabs is highly nonlinear (as for redundant members failing in shear), and the crack openings are to a large extent dependent on local and structural tension-stiffening effects. This deviates the actual behaviour from the one predicted by LEFM and modifies the influence of size effect, which becomes less significant than according to LEFM. In this paper, this phenomenon is investigated by means of the CSCT, providing a consistent frame to analyse size and strain effects accounting for realistic slab responses.