A theoretical approach is developed which describes the growth kinetics of thin films of near noble metal silicide (especially of cobalt silicide (Co2Si) and nickel silicide (Ni2Si)) and refractory metal silicide (particularly of tungsten disilicide (WSi2) and vanadium disilicide (VSi2)) at the interfaces of metal silicon system. In this approach, metal species are presented as A-atoms, silicon as B-atoms, and silicide as AB-compound. The AB-compound is formed as a result of chemical transformation between A- and B-atoms at the reaction interfaces A/AB and AB/B. The growth of AB-compound at the interfaces occurs in two stages. The first growth stage is reaction controlled stage which takes place at the interface with excess A or B-atoms and the second stage is diffusion limited stage which occurs at both interfaces. The critical thickness of AB-compound and the corresponding time is determined at the transition point between the two growth stages. The result that follows from this approach shows that the growth kinetics of any growing silicides depends on the number of kinds of dominant diffusing species in the silicide layer and also on their number densities at the reaction interface. This result shows a linear-parabolic growth kinetics for WSi2, VSi2, Co2Si, and Ni2Si and it is in good agreement with experiment.