The Lanczos algorithm is one of the most widely used methods for finding a small number of the extremal eigenvalues and associated eigenvectors of large, sparse, symmetric matrices. In this paper the performance on two parallel machines with different architectures of a modified version of the algorithm which incorporates a novel convergence monitoring method is assessed. The investigation has been carried out using a shared memory Convex C3840 with two processors and a 16-node Intel iPSC/860 hypercube. It is shown that parallel implementations of the modified algorithm can efficiently exploit the facilities provided by both machines. However, there are significant architecture dependent considerations which favour the use of the shared memory machine for the solution of general instances of the problem. These considerations relate to the cost of inter-processor communication and the limited availability of fast memory on the distributed memory machine.