Wide use of various porous materials in construction engineering applications requires development of up to date methods of non-destructive characterization and optimization of such materials. This work explores an approach to modeling of fracture of a brittle porous material. Available 3D digital data on the specimen geometry is converted into uniform finite element mesh consisting purely of elements of cubic shape. Fracture model is based on a series of linear solutions. Thus approach to linear modeling described in the previous papers could be utilized. Fracture is modeled by consecutive element erosion. A special element erosion criterion is established to avoid finite element size dependency. Two speed-up algorithms are proposed and tested. The approach described can be used for modeling fracture of uniform construction materials, also materials with inclusions under various mechanical and thermal loads.