Underground projects are typically performed in nonpersistent jointed rock masses. Excavation of tunnels or chambers causes crack initiation, propagation and coalescence, resulting in the instability and destruction of surrounding rocks. The failure behaviour of rocks is complicated owing to the interaction between holes and joints. Therefore, understanding the failure characteristics of holes in jointed rock masses is essential. In this paper, the mechanical characteristics of a jointed rock mass with double circular holes under uniaxial loading was investigated using the discrete element method. The effects of different joint parameters on the strength and failure behaviour of the jointed rock mass with double circular holes were studied. The results show that the existence of joints degrades the mechanical behaviour of the rock mass. Specifically, the peak strength and elastic modulus of the specimens show a “U” shape change with the joint dip angle and reach the minimum value when the angle is 30°. With an increase in joint spacing, the peak strength and elastic modulus increase gradually. An investigation of the crack coalescence process and displacement field of the specimens reveal the crack propagation mechanism based on the interaction between holes and joints under uniaxial loading. Five types of crack coalescence among the holes and adjacent joints were summarized. Four typical failure modes were observed: tensile failure across joints, block rotation failure around holes, shear failure through joint planes and tensile–shear mixed failure through holes.