This paper introduces a newly developed three-dimensional Material Failure Process Analysis code, MFPA3D to model the failure processes of brittle materials, such as concrete, ceramics, fibrous materials, and rocks. This numerical code, based on a stress analysis method (finite element method) and a material failure constitutive law, can be taken as a tool in numerical modeling analysis to enhance our understanding of the failure mechanisms of brittle materials. Properties of material heterogeneity are taken into account. The material is discretized into numerous small elements with fixed size. Fracture behavior can be modeled by reducing the material stiffness and strength after the peak strength of the material has been reached. The evolution of the cracking process down to full fracture implies strain softening, which describes the post-peak gradual decline of stress at increasing strain. In the present study, a Mohr-Coulomb criterion envelop with a tension cut-off is used so that the element may fail either in shear or in tension. Simulated fracture or crack patterns of two examples are found quite realistic, and the results strongly depend on the heterogeneity level.