During the manufacturing of a power cable insulated with the cross-linkable polyethylene, the hot polymer is applied to the conductor by extrusion, below temperatures of the rapid cross-linking. The coated cable passes into a high-pressure tube (filled with nitrogen under the pressure of 10 bar) in order to heat up the insulation to temperatures at which the cross-linking agent is highly active. This is the continuous vulcanization (CV) tube. Changes of process variables associated with the CV tube can cause changes in the physical properties, the aging characteristics, and especially the heat resistance of the cable insulation. Performance of insulating compounds in this area of the cross-linking process can determine maximum output rates of a power cable manufacturing facility. The mathematical model describes cross-linking process in the vulcanization tube, which is in fact a tubular reactor. In the vulcanization tube heat is transferred by convection, conduction and radiation. Also, the reaction heat is liberated by the chemical reaction and the heat balance describes all four impacts. Formal part of the mathematical model is a material balance that describes the reactions kinetics. Heat and mole balance are connected with reaction rate and mathematically present a system of partial differential equations which will be numerically solved for chosen boundary conditions, both for the reaction part and for the cooling part of a process. On the basis of the real process parameters and the presented mathematical model simulation of the process was conducted. From the presented simulation the optimal process parameters such as process temperatures, cable linear velocity (u) and cable cooling properties of CV line are predicted and evaluated. (C) 2007 Elsevier B.V. All rights reserved.