A method of interpolation of the boundary variables that uses spline functions associated with singular elements is presented. This method can be used in boundary element method analysis of 2-D problems that have points where the boundary variables present singular behaviour. Singular-ended splines based on cubic splines and Overhauser splines are developed. The former provides Ct-continuity and the latter C-1-continuity across element edges. The potentialities of the methodology are demonstrated analysing the dynamic response of a 2-D rigid footing interacting with a half-space. It is shown that, for a given number of elements at the soil-foundation interface, the singular-ended spline interpolation increases substantially the displacement convergence rate and delivers smoother traction distributions. Copyright (C) 2000 John Wiley & Sons, Ltd.475951967