Computer simulation was carried out to study the morphological change in the lateral habit of polyethylene single crystals grown from the melt. Monte Carlo simulation was utilized for modelling the processes of surface nucleation and step propagation on the growth faces of a two-dimensional crystal with hexagonal packing. Anisotropy of growth was introduced in the simulation by choosing different rates for these processes on the {110} and {100} faces. Depending on the ratio of the step propagation velocity to the rate of increasing width of the growth face, the computer simulation produced curved crystals of truncated lozenge or lenticular shape, both of which have been observed experimentally. The change in morphology has been analysed quantitatively.