In this paper, we describe a method for speeding up an iterative solver for structural analysis using parallel computers. We have improved the sparse matrix used in the factorized sparse approximate inverse (FSAI) method. The sparse matrix in the original method is derived from the matrix to be solved. However, in the sparse matrix that we have developed, we set the terms with minimum influence on the solutions to zero and set the terms with significant influence to a non-zero value. Using the new iterative method, we can obtain the solution in half the time of the conventional CG method. We tested the robustness of this new method into by applying it in shell analysis. The numerical results verified the effectiveness of this solver.