There are so many problems associated with cuttings deposited in the well bore when we using rotary drilling methods to drill some vertical wells, directional wells or even horizontal wells. To overcome these cuttings problems we have to determine a mud minimum rate which has a capability to clean the drilled well bore. This mud minimum rate is sum of the slip velocity and the velocity of the fallen cuttings. It is obvious that velocity of the cuttings are depend on the well bore geometry and the magnitude of the ROP. Hence this cuttings velocity will be constant for a specific well bore. This paper develops Moore's slip velocity of vertical well in order to be used in the inclined well until horizontal well with some corrections of rotary speed and the mud weight by Larsen's slip velocity procedure. The corrections of inclination angle, RPM and the mud weight are obtained from Y axis of cartessian dimensionless plotting of slip velocity with the inclination angle at X axis. Dimensionless slip velocity equals Peden's experiment slip velocity data and Larsen's calculation results for inclined well divided by Moore's slip velocity for vertical well. The paper results a new equation to determine the mud minimum rate which would lift the cuttings in the inclined through horizontal well bore. In the case of inclination angle > 45°, the mud minimum rate of Larsen's method, Larsen's experiment data and Peden's experiment data have no significant difference with this new equation in the paper. On the other hand, at inclination angle < 45°, the new equation results a higher mud minimum rate than all of the methods above resulted.