Coiled tubing (CT) injector head is a key part of CT unit. Friction between gripper blocks and CT offers axial force that runs and retrieves the CT into or out of the wellbore. The CT held by the gripper blocks is loaded by axial force, pressure of inner fluid and gripping force, and is in a complex forcing state. Here it was assumed that all stresses were invariable longitudinally and could be simplified as problem of plane strain. The gripping force acted on the outer surface of CT was set as sinusoidal function along circumference. Stress function was employed to deduce the stress state of CT in gripper blocks. The effects of gripping force, inner pressure and axial force on CT strength were studied, and yield limit curves of the CT were presented by Mises yield criterion. These results offer referring data for minimizes the risk of scarring or mashing the CT.