A discrete element model (DEM) of SiC ceramics containing two parallel flaws was used to study crack coalescence under uniaxial compression with different flaw inclination angles, ligament lengths, and ligament angles. A relationship is proposed between coalescence stress state, flaw inclination angle, and horizontal component of the ligament length during the failure process. The effects of coplanar flaws on various characteristics of the specimen, viz. compressive strength, Young’s modulus, crack initiation stress, and Poisson’s ratio, were studied. Coalescence modes between two parallel flaws observed in the DEM model were in good agreement with nine crack coalescence categories summarized in experimental studies. Meanwhile, the corresponding stress state at the moment of coalescence can be classified into three types – pre-peak, mid-peak, and post-peak. The results also showed that the horizontal component d of the ligament length of parallel flaws significantly influences the coalescence stress state. When parallel flaws overlap in the loading direction (d < 0), with an increase in the inclination angle, the occurrence of crack coalescence changes from pre-peak period to mid-peak period and post-peak period and eventually to non-coalescence. When d = 0, coalescence between the flaw pair mainly occurs before the peak stress and the corresponding flaw geometries are the most dangerous. As distance d increases, the possibility of crack coalescence decreases.