Two computer subroutine packages for the analytic rotation of a factor matrix, A(p x m), are described. The first program uses the Flectcher (1970) gradient method, and the second uses the Polak-Ribiere (Polak, 1971) gradient method. The calculations in both programs involve the optimization of a function of free parameters. The result is a transformation matrix, T(m x m), giving us the rotated factor matrix. AT(p x m). The advantage of the Fletcher method, a modification of the Fletcher-Powell (1963) method, is that convergence is more rapid than with the Polak-Ribiere method. However, since Fletcher's method builds up an inverse Hessian matrix and the Polak-Ribiere method does not, more computer storage has to be used in the first program than in the second. Therefore, when m is large, the Polak-Ribiere method will have to be used because of storage considerations. Listings of subroutine ROTATE with subprograms using both methods are provided in an appendix. Details of the author's experience with both gradient methods are also given.