The literature available on gear tooth contact stress problems is not very extensive and that available does not explain the method by which analysis was carried out. In this paper an attempt has been made to study the contact stresses of a pair of mating gear teeth, under static conditions, by using a two-dimensional finite element method and the Lagrangian multiplier technique. The contact condition at the neighbouring node pair, namely, the contact existing over a number of node pairs in the contact zone, has been considered. To study the effect of friction between the mating gear teeth a range of average static friction coefficients, from 0.0 to 0.3, has been considered. The actual length of contact against the calculated length of contact is discussed. The variation of contact stress along the contact surface in a direction normal to the mating surfaces, which will give an idea about the depth of hardening required, is also presented. © 1994 Elsevier Science Ltd.