Slope instability and landslides can be catastrophic events often leading to loss of life and property. To assess the risks of slope failures, it is often desired that the dynamic process of slope failure can be simulated. This paper proposes a Granular Contact Dynamics (GCD) approach based on variational principles and implicit time integration to simulate the failure process of slopes. The method has the ability to simulate fracture initiation and development (i.e., progressive failure process) and allows the consequence of slope failures to be assessed quantitatively. A two dimensional example is given to demonstrate the method.