The complex fracturing responses of a single flaw embedded in rock-like materials under compression are investigated using a bond-based peridynamic methodology. Peridynamics is found to be very effective for the investigation of rock fracture. The influences of the flaw inclination angle and the mechanisms of the wing crack propagation are discussed with the experimental data and the simulation results. It is investigated that the secondary cracks develop shear cracks or shear zones where the energy input controls the initiation and propagation of the secondary shear cracks. The comparative study of the experimental results and the peridynamics simulation results shows good agreement.