An in-house finite element code was used to analyse a diametrically compressed isotropic homogeneous Brazilian disc having a central inclined crack with frictional surfaces for the evaluation of its corresponding modes I and II stress intensity factor (SIF). One-half of the disc was successfully idealized. The coefficient of friction between the crack surfaces ranged from 0 to 1 in steps of 0.1. Relative crack length ratios of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 were analysed with crack angles up to 90° in steps of 5°. The crack angle corresponding to the transition from a mixed mode I/II to a pure mode II decreases with increasing the relative crack length ratio. An increase in the relative crack length ratio leads to an increase in the range of crack angles corresponding to a partially closed crack. The crack angle at which fully closed sliding crack surfaces commences is 30° independent of the relative crack length ratio and the friction coefficient. With the same relative crack length ratio and increasing the friction coefficient, there is a corresponding decrease in the crack angle for the maximum mode II SIF. With a decrease in the relative crack length ratio or the friction coefficient, the crack angle beyond which the crack surfaces become in a fully sticking mode decreases resulting in zero mode II SIF. Generally, mode II SIF decreases with increasing the friction coefficient between the crack surfaces. Good agreement has been generally obtained with relevant results found in the literature.