Veined rock masses can be found in porphyry copper deposits like at the El Teniente mine in Chile. Rock masses with cemented joints or veins cannot be accurately represented using the methods commonly applied to predict the deformability and strength of jointed rock masses. Laboratory tests on veined rock andesite from the El Teniente mine have shown that the veins control the fracturing process and strength. In this work, the behavior of veined rock was studied using a numerical model, built in the finite element software ABAQUS. In this analysis, the rock mass was modeled as an assemblage of blocks bonded by layers, representing the intact rock and veins respectively. Uniaxial compression tests on veined core-size specimens were simulated and their results compared to experimental data. The results show good agreement with the experiments in terms of strength, stiffness and mode of failure. After this, a veined rock mass volume was modeled using the orientation of mapped and post-processed discontinuities as input. Simulations of uniaxial and triaxial tests were performed on the modeled veined rock mass. The observed failure mode confirms experimental results, showing that at low confinement the failure is concentrated in the veins and the rupture of intact rock becomes significant at higher confinement. The obtained strength envelope of the veined rock mass is non-linear and its shape is independent of the strength of the intact rock; however, the Hoek-Brown criterion did not fit the results. The residual strength of the veined rock approximated the residual strength of the intact rock, agreeing with previously reported observations in jointed rock.