A new mass conservative mesoscale model for the simulation of fracture of solid materials has been developed. Our representation of solids by spring networks contains two degrees of freedom necessary to match real material properties and exhibits a stable Poisson ratio. The algorithm is based on the energy minimization of the network of triangular springs with critical strain and splitting of overstressed bonds and connected to them nodes ensuring the conservation of mass during the crack evolution. An algorithm to resolve the mesh folding and overlapping for the simulation of compressed materials has been developed by introducing special energy penalty terms. The main emphasis of the research is on the study of brittle fracture but elasto-plastic models for springs have also been developed for the simulation of plastic deformations with limited shear bands. Two regimes of the brittle fracture have been onsidered: adiabatically slow deformation and breakup and instantaneously fast deformation and the formation and propagation of cracks in stressed materials. Parallel software for the fracture of brittle materials under strain has been developed with the integration of packages TAO and Global Arrays. A Schwartz-type overlapping domain decomposition and the corresponding acceleration techniques have also been studied. Three different visualization techniques have been developed to capture details of fractured zones in 3D. The software has been applied to the simulation of fracture of solids under slow stretching deformations, the rapid disintegration of highly tempered glasses in the phenomenon called the Prince Rupert Drop, and the fracture of thin brittle discs hit by high velocity projectiles. The bifurcation of the fracture dynamics from the growth of the comminuted zone to the propagation of isolated radial cracks, typical for the fracture of glass sheets and thin ceramic plates hit by projectiles, has been reproduced in our numerical experiments and scaling studies involving the change of material properties and projectile velocity have been performed. The fracture model has also been used in a coupled multiscale simulation of the nuclear fuel rod failure within a study of nuclear reactor safety issues.