As jointed rocks consist of joints embedded within intact rock blocks, their behavior depends on the behaviors of the joints and the intact rock blocks. In a jointed rock, there are two levels of heterogeneity within the jointed rocks due to the differences in properties between the rock blocks and the joints at a macro-scale, and within the intact rock blocks due to difference in the randomly-distributed flaws at a meso-scale. In this paper, numerical tests on plane stress numerical specimens with an embedded, partially-spanning joint are reported. The individual influence of three parameters relating to the geometry of partially-spanning joints: joint location, joint orientation and trace length was studied. In the simulations, the joints were modeled by elements with low moduli and strengths, whereas the heterogeneity of the rock properties of the intact rock block was taken into account by assuming that they obey the Weibull distribution. The numerical simulations not only agreed well with the experimental results, but also duplicated the complete rupture process of samples with the stress evolution and tempo-spatial distribution of damage events. The numerical results show that there is an approximately linear relationship between the location of the terminus of the partially-spanning joint with respect to the end of the sample (joint location) and the compressive strength of the partially-cut sample, whereby failure stress increases with increasing joint location value. With respect to joint orientation, the simulations show that the minimum compressive strength occurs for a joint angle of 45°, and that compressive strength increases with both increasing joint angle and decreasing joint angle from this critical value of 45°. In relation to the joint trace length, the numerical results reveal that the compressive strength of partially-cut specimens is correlated with the joint trace length using an approximately linear relationship. © 2013 Elsevier B.V.