The profiling process of a friction force microscope (FFM) tip scanning a NaF (001) surface is simulated using a simple model for the FFM based on the solution of the equations of motion. Complete friction force microscopy images as well as individual scan lines are calculated using a model potential for the tip-sample interaction. The nature of the movement of the tip in the interaction potential is analysed and demonstrates the two-dimensional character of the occurring lateral forces. Comparison with recent experimental studies shows good agreement of simulations and experimentally obtained data.