We present a novel class of spatial models of cell movement and arrangement applied to the two-dimensional cellular organization of the intestinal crypt. The model differs from earlier approaches in using a dynamic movement on a lattice-free cylindrical surface. Cell movement is a consequence of mitotic activity. Cells interact by viscoelastic forces. Voronoi tessellation permits simulations of individual cell boundaries. Simulations can be compared with experimental data obtained from cell scoring in sections. Simulation studies show that the model is consistent with the experimental results for the spatial distribution of labelling indices, mitotic indices and other observed phenomena using a fixed number of stem cells and a fixed number of transit cell divisions.