Abstract: The study of crack propagation through the cracked rock specimen is an important research direction of rock mechanics and geotechnical engineering.In this paper,a single axis compression test of a class of rock samples with two non-parallel cracks is carried out by using the numerical simulation software PFC^2D.By means of statistical crack model,two kinds of coalescence modes are found,which are different from the modes of two parallel cracks.The two crack coalescences occurred when the origin inclined crack and another crack have the overlap part in the horizontal direction.From the mechanical response of the specimen,the peak stress of the specimen is the largest when the horizontal cracks are in the same level and the horizontal cracks located in below or above of the origin inclined crack,and the peak stress of the two sides are approximately symmetric.The coalescence of cracks occurred in the stress has reached or not reached its peak value,and the number of the micro-cracks changes regularly when the stress and strain curves of the specimens are from the plastic to the failure of the specimens.The coalescences of cracks and the number of micro-cracks can predict or reflect the failure of the specimen to a certain extent.By the laboratory tests,we found the same coalescence modes that exist in the numerical simulation and it demonstrates the feasibility of numerical simulation.