The strength of drilling mud filter cakes is a parameter of practical relevance during well construction. This work simulates a ‘hole punch test’ experiment to determine filter cake yield stress. The discrete element model is used to predict the energy needed to push a plunger through the cake. The theoretical data is compared with experimental measurements for cakes with varying particle size and shape. The simulations and experiments both show an increase in yield stress and required energy with decreasing cake porosity and particle size. Adhesion due to liquid bridges was found to contribute significantly to cake strength. A scaling argument is established which indicates that the resistance to plunger motion comes from the particles sheared at the edge of the plunger.