Abstract. Geological surfaces are generally known incompletely and have to be reconstructed by use of interpolation methods. Some of these surfaces may be described by a continuous function z = u ( x , y ) , where z is the vertical coordinate (depth). However, tectonic stresses cause discon­ tinuities (faults) and complicated surfaces (folds). In order to interpolate geological surfaces an algorithm is proposed which uses triangular finite elements. Among all functions satisfying the given constraints ( u and pos­ sibly u x and u y at the data points) the sought function shall minimize an integral, the potential energy of a thin elastic plate.