The subroutine SOK solves a set of N simultaneous linear equations by an essentially iterative method. For the method to converge at a reasonable rate (or at all) the user must choose K(< N), the order of subsidiary equations which are to be obtained from the N given equations. The matrix of coefficients of the K subsidiary equations is inverted using the direct method of Gauss-Jordan. The method is most effective on large sparse matrices that have dominant diagonal terms and for this situation it should be possible to choose K a lot less than N. The method is most advantageous compared to other iterative methods when the trial investigation of typical matrices is worthwhile. For large matrix problems , details are given of a possible compact matrix storage arrangement. For very large matrices, which even when compacted cannot fit in core, the solution procedure is feasible, provided the matrix is available from disk or tape a column at a time. The subroutine is written in FORTRAN for the IBM 360/50 computer.