This article presents a model for the interaction of probe and sample geometries in scanning probe microscope (SPM) imaging. The model is in terms of mathematical morphological operations and serves as a powerful tool for simulating SPM images given the geometric shapes of the scanning probe and the scanned sample. The artifacts produced due to probe geometry can clearly be seen in such simulated images. The model also serves as a basis for a tool through which SPM users can visualize how different probe shapes image a sample of interest. Based on the visualization, users can, for example, choose the most suitable probe shape for scanning a sample. We present several simulated SPM images produced using the model. The model is verified by comparing predicted images of spheres and cylindrical patterns with actual scanning force microscope images of polystyrene spheres and microfabricated cylindrical structures.