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-CT and digital microscope measures of concrete surfaces are used to validate a novel numerical generator of faithful 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 resistence computed numerically matches the prior experimental results of Jacobsen. The presented model does not need any fitting procedure, making it a reliable and physically-based model for shear transfer phenomena in concrete.