We report the results of computations for two–dimensional dambreaks of viscoplastic fluid, focusing on the phenomenology of the collapse, the mode of initial failure, and the final shape of the slump. The volume-of-fluid method is used to evolve the surface of the viscoplastic fluid, and its rheology is captured by either regularizing the viscosity or using an augmented-Lagrangian scheme. We outline a modification to the volume-of-fluid scheme that eliminates resolution problems associated with the no-slip condition applied on the underlying surface. We establish that the regularized and augmented-Lagrangian methods yield comparable results, except for the stress field at the initiation or termination of motion. The numerical results are compared with asymptotic theories valid for relatively shallow or vertically slender flow, with a series of previously reported experiments, and with predictions based on plasticity theory.