This paper includes a solver for a large sparse set of linear algebraic equations which are obtained by the application of the finite element method to static structural problems. Proposed method is a modification of Robust Incomplete Choleski-Conjugate Gradient Method, which belongs to Preconditioned Conjugate Gradient Method suitable for supercomputers. Through a number of numerical experiments the authors show that Robust Incomplete Choleski-Conjugate Gradient Method sometimes fails in to obtain the solutions, secondly they clarify the reason of the failures from the theoretical viewpoint, and finally they propose a modification of the robust method by the introduction of the theoretical result. Proposed method is as effective as the original, and it can overcome the demerit of Robust Method which is clarified through numerical experiments.