Dense linear systems arising from volume integral equations can be effectively solved with iterative solvers. In this article we show how these iterative methods can be parallelized. The performance of the serial code is discussed on a vector system and on a RISC processor. The performance depends very much on the memory architecture. The parallel version of the code is written using MPI. We obtain good parallel speedup when the elements of the coefficient matrix are recomputed during each iteration. The speedup is moderate when a special FFT algorithm is used to compute the matrix-vector product.