The peculiarities of tungsten whisker growth by the diffusion-dislocation and vapour-liquid-solid mechanisms are studied. The model accounts for the basic physical causes of whisker growth in halogen lamps observed in experiments. The simulation by the Monte Carlo technique takes into account local supersaturation fluctuations, caused by certain impurities, their frequency of appearance and their duration. The role of impurities in each of the growth mechanisms is shown and proved by the morphology of whiskers obtained in experiments.