A noniterative algorithm for handling prescribed well bore boundary conditions while pumping or injecting fluid in a three-dimensional heterogeneous aquifer is described. The algorithm is formulated by superimposing conductive one-dimensional line elements representing the well screen onto the three-dimensional matrix elements representing the aquifer. Storage in the well casing is also naturally accommodated by the superposition of the line elements. The numerical algorithm is verified by comparison with results obtained from the solution of Papadopulos and Copper (1967). A large-scale example problem involving groundwater extraction from a partially penetrating pumping well located in a highly heterogeneous confined aquifer is presented to demonstrate the utility of the approach. ¿ American Geophysical Union 1995