The work propases a FP multiscale approach to computational modeling of material failure in concreteMlike structures, made of cement/aggregate-type composite materials. Keeping the approach in a classical homogenization setting, a multiscale model is proposed, which naturally provides a microscopic length-scale to be exported to the macrostructure. There, this length scale is used as regularization parameter in the context of the Continuum Strong Discontinuity Approach to material failure, and finite elements with embedded strong discontinuities (E~ FE M). The resulting technique allows robust modeling of crack propagation at the structural scale, accounting for the mesostructure morphology, supplies proper energy dissipation and solutions independent of the finite element and RVE sizes. Application toa number of examples, in the range from light-aggregate concrete to regular concrete, shows the potentiality of the method.