AbstractWhen large, progressive, deformation occurs under plastic or visco‐plastic conditions, elastic deformations are negligible and the material flows in a viscous manner. The flow is non‐Newtonian and the viscosity is a function of the current strain rates. An effective numerical treatment of such non‐Newtonian flow by the finite element method is indicated here and is illustrated by examples of an extrusion process for which approximate slip line solutions are known.The methodology is extended to the solution of transient, quasi‐static situations and coupling with thermodynamic equations is discussed.A stream function formulation of the problem