In this paper the mathematical model of a modern arc heated Plasma Wind Tunnel used to test parts of space vehicles during the re-entry phase is presented. Due to the complexity of the physical processes arising during the operating of the plant, a number of simplification is proposed to obtain a control design oriented fast and efficient simulation software. Such a software was successfully used during the design phase to become confident with the dynamic behavior of the facility and to achieve a process-control integrated design. During the operating life of the wind tunnel it will be used to support the test engineers in the design of the control laws for the tracking of the desired trajectories in temperature and pressure on the test article. A short description of the test control algorithm which is based on the above model is also provided.