Fracture mechanics can be applied to many engineering fields including civil and mining engineering, where drilling, excavation, fragmentation and cutting of rocks are closely related to the strength, stability and :fracture of rock materials and structures. This study presents an application of fracture mechanics to determine the effect of dimensions on mixed-mode fracture properties of rocks by using the numerical analyses. Using the finite-element results, correction factors were applied to the specimens and a polynomial fit was proposed to evaluate the stress intensity factors of a modified version of Arcan specimen with a crack subjected to mixed mode loading. The finite element analyses of bonded joints were also studied for different thickness and crack length. The mixed-mode fracture toughness tests were carried out by using rectangular specimens over a wide range of loading angles. Using the finite element results, non-dimensional stress intensity factors applied to the rectangular fracture specimen. It is also shown that when the ratio of crack length to specimen thickness (a/w) is increased, the stress intensity factors in mode-I and II are raising too. But this growth is tangible in mode-I. On the other hand the proportion of loading in mode-I and II between 60 and 70 degree is same.