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Abstract Granite, an excellent medium for deep geological disposal projects, geothermal systems and geological carbon storage, may be affected by its grain size and pre-existing flaws. Thus, three types of granite specimens with different grain sizes containing two non-coplanar fissures under uniaxial compression were investigated experimentally and numerically. Notably, the ligament angle had more effect on the peak strength than the grain size. With an increasing ligament angle, the angle between the crack and the principal stress did not show an obvious trend for β ≤ 60°, whereas the angle between the crack and the principal stress increased when β ≥ 60°. This trend is similar to that for the peak strength. For the same ligament angle, the angle between the crack and the principal stress increased as the grain size decreased. Based on the micro-structure of the crack surface in the ligament (β = 60°), the hypothesis that a shear crack is more difficult to initiate in coarse granite specimens than in fine granite specimens was presented and verified by experiments and numerical simulations. [ABSTRACT FROM AUTHOR]