In the virtual development process, the assessment and optimization of vehicle suspension and chassis performance are based on the forces that are transferred by the tire from road into the suspension. In this load transfer, the tire is one of the most critical components because the tire has a strong nonlinear behavior and is very difficult to model. For many applications, the description of the inflation pressure as a time dependent quantity is sufficient. However, there are tire applications where it is needed to describe the inflation gas using a dynamic gas equation (Euler or Navier-Stokes). One such example is when the tire model is used in NVH (Noise-Vibration-Harshness) applications where the frequency range extends the 200 Hz range. For passenger car tires, a first mode of the inflation gas is at around 200-250 Hz. This mode couples with the tire structure and yields significant peaks in the spindle force spectrum, which have to be considered in the NVH assessment of a vehicle. In this paper, we are modeling the inflation gas of a tire by an isentropic compressible Euler equation and couple it to the tire dynamics in the nonlinear transient application range. After validation of the overall model by comparison with respective measurements, the authors are also describing how one can derive a linear model from the overall transient tire model, which can be used in linear FEM based NVH-tools. It should be pointed out that the tire rotation will yield a split in the aforementioned cavity mode which increases with rotational velocity as is shown by measurements and simulation with and without cavity model.