The motion of frontal disturbances in the atmosphere was studied by the numerical solution of differential equations based upon a two-layer model of an incom pressible fluid on a rotating earth. The density of each layer was assumed to be constant. The upper and lower fluids correspond respectively to warm and cold air. In this first attempt, only the motion of the lower cold air layer is studied by assuming, in effect, that the dynamics of the perturbations in the upper warm air layer can be neglected. The numerical study of this simple mechanical model shows that even though thermodynamic processes have been ignored, the occlusion process, characteristic for warm and cold fronts, develops from an initially sinusoidal frontal pattern. Two cases of different initial conditions were examined.