Analytical expressions are derived for the velocity vector, the stress components and the viscosity function in fully developed channel and pipe flow of Phan-Thien–Tanner (PTT) fluids; both the linearized and the exponential forms of the PTT equation are considered. The solution shows that the wall shear stress of a PTT fluid is substantially smaller than the corresponding value for a Newtonian or upper-convected Maxwell fluid, with implications for comparing predicted and measured values in a non-dimensional form.