A non-conform finite element proposed for viscous fluid flow satisfying zero divergent condition is adapted to our model, This needs some numerical aspects aspects which characterize our algorithm and precise the method of solution on digital computers. The variational formulation of the model permits the use of optimization techniques. A descent technique, thqt of Flecher-Reeves with re-initalization and a proposed line search. t-chnique are used. For our model the vanishing divergence condition is not sufficient to sustain our problem as an unconstrained optimization problem. A penalty method (exterior penalty function) is now necessary for the numerical solution. Apractical example is solved using our algorithm and the corresponding stress distributions are obtained.