Discontinuities are inherent components of rock masses and can range from fissures to large faults. Single fissures, the so-called flaws, may affect the mechanical behavior of rock mass, crack initiation, and propagation. In this paper, numerical investigations have been conducted on central-flawed cylindrical specimens subjected to axial loading to investigate the effect of flaw angle (α), length (2a), and aperture (A) on their mechanical behavior and crack development. Particle Flow Code (PFC3D) was adopted to investigate the cracking process of the cylindrical specimens and maximum principal stresses at flaw tips. The numerical models are calibrated and verified using extensive experimental tests. The results show that increasing α, UCS, and E increase while increasing 2a decreases UCS and E, and A does not affect these two parameters. Moreover, numerical simulations reveal that as α rises, the three principal stresses generally fall when 2a = 13 and 26 mm. σ1 and σ3 peak at α = 45°, and σ2 reaches a maximum at α = 30° in models with 2a = 39 mm. The cracking patterns resulting from both methods are highly consistent in that tensile cracks type 1 mainly form at α = 15° to 75°, and tensile cracks type 3 are dominant at other angles. Finally, it is concluded that flaw aperture scarcely affects failure patterns.