In concrete structures, opened cracks contribute significantly to the transfer of shear and normal stresses through the contact forces occurring between fractured surfaces. Such contact forces are due to protruding asperities, engaged by interlocking and friction. In this paper, the role played by roughness on shear resistance is investigated numerically. First, micro computed tomography and digital microscope measures of concrete surfaces are used to validate a novel numerical generator of realistic cracked concrete surfaces. Secondly, a contact solver based on the boundary integral approach allows an extremely fine description of typical cracked surface topologies. Roughness changes drastically the predictions, so that the shear resistance computed numerically matches the prior experimental results reported in the literature. The proposed model does not need any fitting procedure, making it a reliable and physically based method for predicting shear transfer phenomena in concrete. An empirical power-law predicting the shear resistance in concrete is a direct outcome, which accounts for micro-scale roughness and aggregate distribution.