Summary A rapid digital computing method for the direct calculation of the shapes of two-dimensional sedimentary basins of known density contrast from their residual gravity anomalies is described. In conclusion an example of the use of the method in determining the shape of the Dumfries New Red Sandstone basin (South Scotland) is given. I. Introduction Two rapid computing methods for the interpretation of effectively twodimensional gravity anomalies have recently been developed. The first method enables the calculation of the theoretical anomalies of specified two-dimensional shapes bounded by a connected polygonal series of straight lines. A programme similar in principle has already been developed and described by Talwani & others (1959) and therefore this method need not be described. The second method enables the shapes of two-dimensional sedimentary basins to be obtained directly from the regionally corrected gravity anomalies profile. This is logically a development from the first method and is based on the principle of successive approximation for the removal of residuals. This method is described in the following account and in conclusion an example of its use is given. 2. Calculation of shapes of sedimentary basins