In this paper, penalty finite element method is applied to the simulation of three-dimensional incompressible viscous steady flow, and the program is coded for analysis of three-dimensional flow process of plastic melt in extrusion die. Slit die is typical in polymer extrusion process, and the relevant part is used widely. Because the flow law is different for various polymers with different rheological character even in the same die, the polymer flow in slit die is simulated for Newtonian fluid and power-law fluid by the program and ANSYS, respectively. Flow laws of two kinds of fluid are compared, and the result shows that the non-uniform velocity distribution in outlet is caused by the non-Newtonian effect of material. The penalty factor is important for the penalty finite element model, which decides the precision and efficiency to a great extent. The proper penalty value is decided by some factors, for example, the character of the whole equations and geometric model. Numerical solution with change of penalty value and viscosity is analyzed, and the result shows that the penalty value should be suited with viscosity in special range for penalty finite element model. The experiment has been developed, and the velocity distribution in outlet of slit die is measured. The result of finite element analysis is consistent with experimental result basically, and the reason of result divergence of the two ways is analyzed. The results show that the given model is suited for the polymer extrusion process, and the advice of the selection of penalty value is instructional for penalty element model.