Rock generally contains various micro-cracks, fissures, pores, joints, and other defects. These defects affect the mechanical properties of rock. In order to clarify the influence of native fissures on rock deformation and failure modes, a laboratory study was carried out using the fissured dolomite, and acoustic wave velocity measurement and natural water absorption tests were conducted to determine the wave velocity and open porosity of the rock specimens. A series of uniaxial compression tests were conducted using the Rock Mechanics Rigidity Servo Testing System, and the strength and deformation characteristics and failure modes of the rock were analysed. The test results show that wave velocity, uniaxial compressive strength, and elastic modulus correlate well with open porosity by negative logarithm relations, and the correlation coefficients range from 0,699 to 0,848. When the stress reaches approximately 50 % of the uniaxial compressive strength, the number of acoustic emission increases substantially; when the stress reaches 10 MPa, the internal damage of the specimens begins to occur. The analysis of the post-failure morphology of the specimens suggest that three types of failure modes, i.e., tension, tension-shear mixed, and shear failures, are possible under uniaxial compression for the tested dolomite. The failure modes are closely related to the initial state of the fissure distribution in the rock. The conclusions obtained in this study provide significant reference for the stability analysis of fractured rock in rock engineering.