  We set out the theory and discretization scheme for a new finite-element
computer code, written specifically for the simulation of maser sources. The
code was used to compute fractional inversions at each node of a 3-D domain for
a range of optical thicknesses. Saturation behaviour of the nodes with regard
to location and optical depth were broadly as expected. We have demonstrated
via formal solutions of the radiative transfer equation that the apparent size
of the model maser cloud decreases as expected with optical depth as viewed by
a distant observer. Simulations of rotation of the cloud allowed the
construction of light-curves for a number of observable quantities. Rotation of
the model cloud may be a reasonable model for quasi-periodic variability, but
cannot explain periodic flaring.
