The structural properties of external galaxies may be investigated using a model to generate the predicted number of stars as a function of apparent magnitude in any field in the galaxy. An implementation of such a model is explained in detail and is then tested against observations of M31. These data consist of several CCD images of several fields in M31 along the minor axis, with one field along a “diagonal”. Additional data for 5 fields along the major axis was also made available. Modelling of two galaxy components — the spheroid and the disk — is undertaken. A spheroid density normalization of 3.1 x 10⁻⁶ stars pc⁻³ at 10 kpc is derived for two of the spheroid fields. The data for the field along the diagonal gives a density approximately 1.5 greater than this, possibly implying that the spheroid of M31 is inhomogenous. The spheroid axial ratio can be constrained to between 0.4 and 0.7, values similar to previous works. The effective radius cannot be constrained as well because it has a much smaller effect on the observed number counts. It is also noted that changes in these parameters can compensate for changes in the density normalization. Modeffing the disk counts is more problematical — the reasons for this are discussed in some detail. The disk density normalization is found to be approximately 1.5 x 10⁻⁴ stars pc⁻³ at 10 kpc giving a disk to spheroid density ratio of about 48:1. Using models run over grids of scale height and scale length it is found that the scale height is limited to between 50 and 400 pc, the scale length constrained to between 5 and 7 kpc.