Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil‐water interface to rise up towards the wells. A three‐dimensional boundary integral formulation is presented for calculating the steady interface shape when the oil wells are represented by point sinks. Sophisticated integration techniques are implemented in an effort to obtain accurate results. In particular, the efficiency of various integration methods are compared for this problem, includingQUADPACKroutines, adaptive methods based on the IMT rule, the Kronrod rule, the method of degenerate quadrilaterals, and the Gauss‐Rational rule for infinite integrals. Numerical results for various general multi‐sink distributions are discussed, as are some further results for the axisymmetric single well problem. ©1996 American Institute of Physics.