The system of pores of autoclaved aerated concrete (AAC) is described by the so-called cherry-pit model, a random system of partially interpenetrating spheres. For the simulation of fracture processes, the solid phase is approximated by an irregular spatial network of beams obtained by means of the so-called radical tessellation with respect to the pore spheres. FE calculations using standard software (ANSYS) yield the strain energies of the beams. These energies are used as fracture criterion according to which highly loaded beams are considered as broken and are removed from the network. The paper investigates the relationship between mean fracture strength and microstructure for structures close to real AAC samples and virtual structures with particular geometrical properties.