Abstract: In a simultaneous-linear-equations solving method of calculating the numerical solutions of simultaneous linear equations having a coefficient matrix, all the elements of coefficient matrix elements including zero elements and all the elements of right-side vector elements are stored into an array. Next, a non-zero-structure-specifying index table is created which indicates the row number of a terminal-end non-zero element in each column and the column number of a terminal-end non-zero element in each row within the array. Moreover, a decomposition processing is executed toward the elements existing within a range indicated by the created index table. Finally, a forward/backward substitution processing is executed toward the coefficient matrix elements subjected to the decomposition processing and the right-side vector elements stored into the array, thereby determining the numerical solutions.