In this study, pre-cracked cubic specimens of concrete materials were especially prepared in a concrete laboratory to study the breaking process of brittle solids. Then, the linear elastic fracture mechanics concept of the stress intensity factor and the experimental methods were used to investigate the failure mechanism of pre-cracked concrete specimens under compression. The crack propagation mechanism and the ultimate strengths of these specimens were obtained in the laboratory. Several numerical analyses were also carried out on the pre-cracked specimens, using the finite element method and ABAQUS software package. The damage location and convergence diagram of the differential evolutionary algorithm under mode I, II, III or IV loading conditions were investigated for the cubic pre-cracked concrete specimens containing a single center crack with different inclination angles. The crack propagation mechanisms obtained numerically were compared with the corresponding experimental ones proving the proposed method’s feasibility.