The engineering calculation and construction of the extrusion tool in the form of cylindrical forming channels with sudden narrowing is associated with the determination of the coefficient of resistance of sudden narrowing and local pressure losses. The available theoretical and experimental data on the values of the resistance coefficient of sudden narrowing are contradictory, approximate in nature and, in some cases, do not take into account the rheological properties of the liquid. Their use to calculate local pressure losses under laminar flow conditions leads to significant errors. To eliminate the indicated problems, a mathematical statement of the problem of isothermal stationary laminar flow of non-Newtonian non-compressible fluid in an axisymmetric channel with sudden narrowing was formulated. The mathematical model of flow in spatial formulation is formalized in the form of equations for preserving momentum and mass. As a rheological model, the Carreau model is taken, taking into account the presence of finite viscosity values at marginal shear rates. The numerical solution of the problem was performed by the finite element method using the Comsol MultiphysicsTM CFD modeling package. As a result of the solution, the picture of the current of the non-Newtonian medium was restored in the form of the distribution of current lines, kinematic and dynamic flow parameters. The impact of Reynolds number on change of geometric characteristics of flow structure, kinematic and dynamic flow parameters was evaluated. Values of local resistance coefficient and pressure losses for overcoming sudden narrowing for selected flow modes are calculated. The results of computational experiments are summarized in the form of a criterion ratio for calculating the coefficient of local resistances depending on the Reynolds number.