The block preconditioned conjugate gradient methods are very effective to solve the linear systems arising from the discretization of elliptic PDE. Nevertheless, the solution of the linear system Ms = r, to get the preconditioned residual, is a 'bottleneck', on vector processors. In this paper, we show how to modify the algorithm, in order to get better performances, on such computers. Numerical tests carried out on a CRAY X-MP/48 are presented, in order to give numerical evidence. © 1990.