The paper presents a mathematical model 
for an inelastic fluid whose apparent 
viscosity is a polynomial function of 
the invariants of the rate of strain tensor. 
Starting with the constitutive equation, 
the two-dimensional boundary layer equations 
for the flow near a moving flat surface have 
been derived. The system of nonlinear partial 
differential equations for this flow has been 
subjected to a similarity analysis. 
This leads to a nonlinear ordinary differential 
equation ({\sc ode}) involving the similarity 
functions as well as a non-Newtonian parameter 
$K$ and another parameter $r$($= W/U$, 
$W$ and $U$ being the wall velocity and the 
free-stream velocity, respectively). 
For $r \ll 1$, two nonlinear {\sc ode}s 
governing the similarity functions have been 
derived. These equations have been subjected 
to a perturbation analysis in terms of $K$. 
The resulting systems of two-point boundary 
value problems have been solved using standard 
numerical techniques. The boundary layer 
velocity profiles have been presented graphically.