Developing classical works, we propose a model to describe the evolution with time, of the profile of a growing hillock whose initial shape is known. The profile is the envelope of the steps originated at a dislocation line, so its evolution is related to the movement of the steps as determined by the surface diffusion followed by the integration of the growth units in the kinks. When impurities poison the kinks the profile is determined also by the kinetics of impurities adsorption. In the model the kinetic processes are described in terms of several parameters. An example of a calculated profile is presented and discussed. It is suggested that simulations performed varying the values of the parameters can help to understand hillocks morphology and to asses the growth mechanism.