Abstract The surface tension of transition metals is computed as a function of the filling of the d band in the tight binding limit, using an expansion of the density of states in its moments. First we illustrate the possibilities of this method of moments in doing a complete calculation for a non-degenerate band of a simple cubic crystal cut by a (100) plane. We show that the knowledge of the variation of the first few moments of the density of states is enough to obtain a good estimate of the surface tension, whatever is the filling of the band. We use this to study the surface tension of transition metals and compare our results to a broken bond model. In particular, we compute it for fcc nickel, and bcc chromium and α iron, and obtain some agreement with the experimental results.