Stick- slip is the continuous stopping& release of the Bit/BHA due to the irregular down-hole rotation prompted by the existing relationship between the friction torque and the torque applied from the surface to free the bit.

   Friction coefficient between BHA and wellbore is the main player of stick slip amount, which can be mitigated by support a good lubricators as additives in drilling mud.

   Mathematical (or empirical) solves should be done through adjusting all parameters which supposed to reduce stick- slip as low as possible using different models, one of the main parameters is drilling mud. As per Nanoparticles drilling fluid is a new technology that offers high performance it’s necessary to find out the relationship between the use of Nano fluid and the minimum stick- slip vibration. In this study (multiwall carbon Nano tube) will be used as a Nanoparticles in Fresh water bentonite mud and polymer mud by five tests per each one to find out the coefficient of friction and used it in a special torque and drag software as a part of drilling vertical well simulation to calculate expected bottom hole torque within five different Nano concentration per each mud type. In fresh water bentonite mud torque reduction was from 4000 ft-lb to 3500 ft-lb, while in polymer mud torque failed and didn’t reduce, so it raised from 2050.88 ft-lb to be around 2200 ft-lb.