Some iterative methods have been proposed for solving a linear system of equations Ax=b. From the viewpoint of mathematics, emphasis is put upon high convergence rate. However, when these methods are implemented on vector or parallel computers, it is not always the case that we can solve the problems faster using a method with higher convergence rate, since vectorizability and parallelizability are important factors on these computers. We have implemented some algorithms, Including the Jacobi method, Gauss-Seidel method, successive overrelaxation (SOR) method, conjugate gradient method, and preconditioned conjugate gradient method, on the Cray X-MP EA/116se and Alliant FX/40 in Fortran language. The performance of code with and without vectorization or parallelization are compared in million floating-point operations per second (Mflops). Some experimental results are also compared among different algorithms: execution time, number of iterations, and number of floating-point operations. In passing, we compare system performance on the Cray and Alliant computers for some specific problems.