[en] Line successive over relaxation (LSOR) is an iterative method for solving elliptic differential equations. LSOR takes advantage of the CRAY vector capabilities as compared to the point successive over relaxation (SOR) method, which does not vectorize. The substantial advantages of LSOR on a vectorizing machine are not well-known, except in the field of aerodynamics. By minor modification of the traditional SOR elliptic equation solver, we find that in certain coordinates an increase of a factor of two or greater in convergence time can be realized. As a model problem for comparison of SOR and LSOR, the numerical solution of Poisson's equation will be reviewed in Sec. II. In Sec. III, we discuss the decreased computation time on the National Fusion Energy Computer Center (NMFECC) CRAY computers found with LSOR applied to the iterative solution of plasma equilibria. In Sec. IV, the conditions for which LSOR is most useful are summarized