Rock slope failure is a complex process that usually involves both opening/sliding along pre-existing discontinuities as well as fracturing of intact rock bridges. Discontinuity persistence is an important factor governing rock slope instabilities. However, traditional slope failure analysis assumes persistent discontinuities, and rock slope fails along a predefined persistent continuous potential failure surface because of the limitations of the analysis tools. This paper proposes the numerical manifold method (NMM) incorporated with a Mohr–Coulomb criterion-based fracturing algorithm to simulate the progressive failure of rock slopes with non-persistent joints. Detailed fracturing algorithm is first presented. Then, the NMM enabling fracturing is calibrated through simulating an edge-cracked plate and the Brazilian test. Lastly, the developed code is applied to investigate the failure process of rock slopes involving non-persistent joints. Numerical results indicate that the proposed method can capture the opening/sliding along existing discontinuities, the fracturing in intact rock bridges and the final kinematic release. Progressive slope failure is well exhibited. Copyright © 2013 John Wiley & Sons, Ltd.