Extrusion through mathematically contoured die plays a critical role in improvement of surface integrity of extruded product. There is gradual deformation which results in the uniform microstructure. In the present investigation non-dimensional extrusion pressure and optimum die length for cosine die profile has been obtained by three dimensional upper bound method using dual stream function method for different reductions. The theoretical modeling has been validated with experiments. The experimental results are found to be compatible with the theory.