As an aid to understanding the mechanism for the field-induced alignment of the smectic A phase we have attempted to simulate this process for the Gay-Berne model mesogen GB(4.4,20.0,1,1). The results for the quasi-dynamical behaviour of the alignment process obtained from a constant pressure-constant temperature Monte Carlo simulation are discussed. It. is found that the molecules realign parallel to the field without destroying the layer structure and, more or less, as a monodomain in the simulations. This is qualitatively in agreement with the results obtained from recent deuterium NMR and small angle X-ray experiments. In addition, the relationship between the box shape and structures formed during the alignment process is discussed. The choice of box is found to be important for the simulation of the field-induced alignment process.