This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assembly’, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices—up to a small variation introduced by compression—so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique. Copyright © 2003 John Wiley & Sons, Ltd.