The rock masses have naturally a large number of cracks and discontinuities which cause to be prone to damage under dynamic loading. The earthquake as a kind of dynamic loading may propagate the inherent cracks in rock masses and leads to failure of the rock structures such as mines, oil and gas wells, tunnels, dams, etc. Therefore, the fracture of rock masses due to cracks under earthquake should be considered by civil, mining and even mechanical engineers and researchers. Fracture mechanics as a branch of mechanical engineering science has been frequently employed for investigating the fracture behaviour of cracked rock structures. According to the orientation of crack relative to applied load, the cracked parts may be subjected to pure or combined mode loading I, II and III. The underground rock masses are often subjected to a compressive loading due to the pressure of upper rock masses. In the first sight, the crack flanks under compression are pressured together and the geometry discontinuity is vanished. However, the crack faces may be subjected to sliding loading and the vulnerability of cracked rock masses is still remained. Therefore, the fracture analysis of cracked rock masses under compressionshear loading should be investigated. Similar to the mixed mode I/II loading, there are several studies in the literature investigated the fracture of cracked specimens under Compression-shear loading both experimentally (Al-Shayea, 2005) and theoretically (Li et al., 2009). From the theoretical viewpoint, the compression is considered as a compressive stress in the stress field around the crack tip and then the fracture criteria based on new stress field is utilized for predicting the fracture resistance of cracked specimens. The aim of this paper is to present a new approach for predicting the fracture load of cracked rock samples under Compression-shear loading. The new approach is based on the maximum tangential stress (MTS) criterion which is one of the classical fracture criteria in fracture mechanics.