The center-cracked Brazilian disc specimens can be used to measure dynamic fracture toughness under pure mode I, pure mode II, or mixed-mode loadings for brittle materials. The pure or differently mixed mode dynamic fracture test can be realized by changing the loading angle θ, which is the inclination angle of the loading diameter with respect to the center crack. The finite element software ANSYS is used to simulate the impact fracture tests of the specimens, and the effect of different types of loads, materials and specimen geometry on the dimensionless dynamic stress intensity factors are investigated. An approximate formula is proposed to calculate the loading angle θII for the pure mode II loading. As for the mixed mode loading, when a ramp load is applied, the stress intensity factors of mode I and mode II have similar curves of time history, and the mixed-mode ratio of mode I to mode II stress intensity factor, i.e. KI(t)/KII(t), is nearly a constant value. The ratios of specimens with different dimensionless crack length under different loading angle are presented. Using these values, the dynamic crack initiation angles β0 can be estimated based on the strain energy density factor criterion, the estimation is in good agreement with the experimental results given in the references.