The mechanical behavior of rock containing parallel non-persistent joint sets was studied using a numerical model. The numerical analysis was performed using the discrete element software UDEC. The use of fictitious joints allowed the inclusion of non-persistent joints in the model domain and simulating the progressive failure due to propagation of existing fractures. The material and joint mechanical parameters used in the model were obtained from experimental results. The results of the numerical model showed good agreement with the strength and failure modes observed in the laboratory. The results showed the large anisotropy in the strength resulting from variation of the joint orientation. Lower strength of the specimens was caused by the coalescence of fractures belonging to parallel joint sets. A correlation was found between geometrical parameters of the joint sets and the contribution of the joint sets strength in the global strength of the specimen. The results suggest that for the same dip angle with respect to the principal stresses; the uniaxial strength depends primarily on the joint spacing and the angle between joints tips and less on the length of the rock bridges (persistency). A relation between joint geometrical parameters was found from which the resulting failure mode can be predicted.