Abstract: An important consideration encountered in the use of the finite element method is how a computational result can be obtained as accurate as possible with the least computation effort for a special problem, especially for a problem of singularity with the character of stress concentration. This is the problem of Optimum Finite Element Discretization developed during the recent decade. In this period a lot of optimization criteria and corresponding procedures were proposed. The purpose of the present paper is to suggest a new effective method for improving the finite element discretization which can avoid the difficulties and shortcomings encountered in a batch-mode operation and doesn't need the special software for computation of contour lines and computer graphic displays. After a relatively simple operation, the grid optimization can be performed by the aid of a feasible direction obtained via opti-mality criteria combined with the one-dimensional search techniques. The computational results of numerical examples presented show that in the best case from an even grid to an optimized grid a gain of the total potential energy was obtained, being equivalent to an increase in the number of degrees of freedom from 40 to 4900. It is obvious from tables and graphics presented that quite satisfactory results are obtainable, no matter whether the global or the local error is concerned.