In this paper we discuss the effect of neglecting relative tangential surface displacements in forming the boundary conditions of elastic contact problems between dissimilar materials. This is one of the known approximations made by Hertz in his original theory. Attempts have been made only recently to build up procedures to take this 'convective' effect into account, for simple plane problems . However, before questioning all the existing solutions for elastically dissimilar contact problems, it is considered important to estimate quantitatively the order of the possible correction. Here a simple iterative procedure is set up to solve frictionless plane contact problems taking into account the 'convective effect'. Attention is focused on the problem of wedge indentation, as this provides a reasonably tractable problem, and on the parabolic indenter, to discuss the Hertzian case. The correction introduced is shown not to be negligible, but is of practical significance only in extreme conditions, viz. frictionless contact and large Dundurs' constant, ฮฒ. In these extreme cases, the maximum correction to the contact are dimension may be of the order of an increase of 10% for the contact area dimension. The effect tends to be more significant for Hertzian indenter and higher order profiles.