Several methods for the evaluation of sphericity error exist. The Minimum Radial Separation (MRS) spheres method is a method that has been studied by several researchers. In the MRS criterion, two concentric spheres at minimum radial separation must be found such that they contain all points on the actual spherical surface. The existing procedures for finding MRS spheres are either too complex and time consuming or do not provide an optimal solution to the sphericity error evaluation problem. In this paper, mathematical optimization concepts are utilized to develop a theory and an algorithm for the evaluation of sphericity error based on MRS criterion. Results indicate that the algorithm is fast and accurate in providing optimal solution to the sphericity error evaluation problem.