In continuous casting, heat flow optimisation in the mould is key to improving the quality of the product and saving production costs. The heat flow both influences and is influenced by several phenomena of a mechanical or a metallurgical nature; hence, these should be included in its optimisation. In particular, shrinkage of the strand and solid phase formation are among those factors most affecting the cooling of the solidifying product. The present paper discusses a model implemented by a software tool that can simulate the shell formation of carbon steel within the mould. This software is able to consider both circular and rectangular billets. The first aim of the software is to simulate the formation of a solid shell in the strand, and the deformations to which this solid is subjected. Deformations are caused by both thermal shrinkage, related to phase changes, and stresses caused by metallostatic pressure or the mould-shell interaction. The simulation can be conducted in two modalities. With straight profiled, tapered moulds, it checks for gap formation between mould and strand and varies the heat extraction accordingly. This first modality appears to be useful for finding optimum casting parameters when mould geometrical features are provided. In the other modality, the developed software can compute the ideal mould contour, once casting parameters are given. The output consists of a temperature map of the billet, history of the plastic deformations of the shell and a map of detachment zones on the mould surface, or the ideal mould contour in the second case.