Hydrodynamic interactions between two identical solid spheres are investigated numerically using a finite element method. The spheres are held fixed relative to each other with the line connecting their centres normal to the flow direction. The method is applied in three-dimensional, at Reynolds numbers 10, 50 and 5 x 10(-7). The drag and interaction coefficients of the spheres are calculated as functions of the distance between the two spheres. The results of the calculations show that, for Reynolds number of 50, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. The results agree with experimental and theoretical data reported for different Reynolds numbers. (C) 2000 Elsevier Science Ltd. All rights reserved.