Non‐Newtonian characteristics of boundary layer flow passing a flat external surface with zero incident angle were studied using Phan‐Thien Tanner (PTT) type constitutive equation with the network theory. Consideration is given to the shear thickening and the shear thickening–thinning characteristics of fluid in the flow problem. The Von Karman integral equation is solved numerically in order to obtain the boundary layer thickness and associated friction coefficient. Two important parameters in the network theory, the segment number and chain slippage parameter, are discussed to investigate their effects on the boundary layer characteristics. The calculated results indicate that there are large jumps of boundary layer thickness at the leading edge of the plate for small slip parameters when the effect of normal stress is not included in the calculation. On the contrary, the jumps are eliminated, particularly for smaller Reynolds number, with the inclusion of the effect of normal stress.