First of all the heterogeneous structure of concrete is described in terms of a multi-level system. To take different effects of crack propagation and crack arresting into consideration, four different levels have been introduced. Conditions for crack propagation in the porous structure of hardened cement paste and in a matrix with inclusions are studied analytically. By using the derived formulae crack formation and failure of lightweight, normal, and high strength concrete are discussed. Computer experiments are described. It is shown that crack propagation and final degradation of composite structures can be simulated realistically. Finally some supplementing experiments are mentioned. Experimental results are in reasonable agreement with theoretical predictions.