We investigate surface-tension-driven fingering of a thin layer of viscoplastic fluid. Using standard lubrication theory we derive an equation for the flow of the film which includes effects of surface tension and yield stress. We obtain traveling-wave solutions to model the advance of a steadily propagating front and then apply a linear stability analysis to model finger growth and to determine the effect of the yield stress. Qualitative agreement is demonstrated between the numerical results and experiments. (c) 2006 Elsevier B.V. All rights reserved.