In this paper, a numerical code, RFPA2D (rock failure process analysis), was used to simulate the initiation and propagation of fractures around a pre-existing single cavity and multiple cavities in brittle rocks. Both static and dynamic loads were applied to the rock specimens to investigate the mechanism of fracture evolution around the cavities for different lateral pressure coefficients. In addition, characteristics of acoustic emission (AE) associated with fracture evolution were simulated. Finally, the evolution and interaction of fractures between multiple cavities were investigated with consideration of stress redistribution and transference in compressive and tensile stress fields. The numerically simulated results reproduced primary tensile, remote, and shear crack fractures, which are in agreement with the experimental results. Moreover, numerical results suggested that both compressive and tensile waves could influence the propagation of tensile cracks; in particular, the reflected tensile wave accelerated the propagation of tensile cracks.