Arc fissure is one of the basic forms of defective rock, where the expansion and evolution mechanism plays an important role in the stability of engineering rock mass under the external load action. Uniaxial compression experiments of sandstone samples that contained various angles of arc fissures (sandstone sample was 80 mm × 160 mm × 30 mm) were performed in order to investigate the effect that arc angle α had on the mechanical properties, the failure mode, and the fracture evolution process of sandstone. The results showed that when arc angle α was increased, the peak strength and the strain of the sandstone samples initially decreased before increasing and the minimum peak strength and strain were reached when α = 15°. The deterioration of the bearing capacity and the number of cracks that appeared during the sandstone loading process decreased as the arc angle of the fissure increased. The arc fissure destruction was primarily initiated from the fragile area of the arch tip. The tensile cracks appeared on the fissure tip and non-tip as the axial force increased. The various arc angle α played an important role in the initiation stress and the rupture evolution of the specimen.