Many techniques for building genetic physical maps of genomes involve collecting and characterising large numbers of genomic extracts. Errors and uncertainties in the data mean that many plausible maps can often be constructed from such data. This paper presents a model, based on minimum message length principles, that can be used for representing such maps. The model is designed to handle fragment length data from clone fingerprinting experiments. Information regarding sequence tagged sites, providing further confirmation of the map structure, can also be incorporated. Results are presented from the application of the model as an objective function for a mapping program. The optimal solution found by the mapping program using this model, is quite similar to that found by a human expert. We also demonstrate how the model can be used to estimate error parameters associated with the mapping process, and to identify weak sections of the map.