In view of the scratches, necks and service life reduction caused by blowout preventer with slip ram during coiled tubing operation, the influence of friction coefficient between coiled tubing and slip ram on its interaction is put forward. A three-dimensional physical model of coiled tubing clamped by slip ram is established, and its calculation model is established based on elastic-plastic mechanics theory. Based on Ramberg-Osgood elastic-plastic model, the maximum Mises stress, axial displacement and contact stress of coiled tubing under various working conditions are analyzed by means of numerical simulation. The results show that increasing friction coefficient properly is beneficial to reduce stress concentration on coiled tubing, to limit axial displacement, to avoid scratching coiled tubing and cracking of slip ram, and to improve the clamping effect of slip ram on coiled tubing. Finally, taking yield strength as the index and combining with the trend change of axial displacement of coiled tubing, the safe range of friction coefficient is 0.4-0.6, which aims to provide reference for safe operation of coiled tubing.