In this paper, the problem of coating wire by withdrawing it from a bath of Phan-Thien-Tanner (PTT) fluid is investigated. The problem is analyzed using (a) the complete form of the Phan-Thien-Tanner (PTT) constitutive equation with a linearized version of the stress coefficient; and (b) the simplified form of the PTT constitutive equation with an exponential version of the stress coefficient. An exact solution of the governing equation is obtained for both cases. The influences of various emerging parameters on the velocity profile, volumetric flow rate, radius of coated wire, shear stress at the surface of the wire, and force required to pull the wire are discussed through graphical illustrations.