Abstract: An optimal algorithm of the generalized Jacobi method is developed to solvethe generalized eigen-problems in the finite element analysis of structuralproblems. Novel operations in this optimal algorithm are adopted to definethe threshold estimation for the off-diagonal elements and the convergencycriteria in the sweeping iterations, so that the present algorithm isapplicable to the original structural problems, not only with thepositive-definite matrices, but also with the general symmetric matrices solong as their eigenvalues are all real numbers. This paper has proved theoptimal algorithm mathematically.