The aim of this paper is to present some computational results for the exterior point simplex algorithm (EPSA). Our implementation was carried out under the C environment. This algorithm seems to be more efficient than the classical primal simplex algorithm (PSA), employing Dantzig’s pivoting rule. Preliminary computational studies on randomly generated sparse linear programs support this belief. Also we use a modification of a recently developed procedure for updating inverse matrices and incorporate it with EPSA. This calculation requires (m2) operations .In our computational study we use the modification of the product form of the inverse which is faster than the classical product form of the inverse.