The aim of this paper is to reproduce the texture of rough surfaces by means of simulations of probabilistic random function models. The studied texture is obtained by a physical process, the electro-erosion discharge. After an introduction to this process and to the characterization of random functions, different morphological models are reviewed and tested: the Boolean random function, the dead leaves random function, the sequential alternate random function, and the dilution random function. They all involve a combination of a Poisson point process and of elementary patterns, the primary random function. For each model, the case of cylinder primary functions is first considered for illustration; then simulations with roughness craters are compared to rough surfaces. The final model involves the use of a repulsion distance in the simulation, as could be expected from the variogram of the data.