Self-excited vibrations of flexible labyrinth seals with compressible flow can be coupled by modal pressure fields. Modal pressure fields cause pressure forces that impact the structure's surfaces outside the labyrinth. Excitation of modal pressure fields is due to periodical changes of flow through the seal's air gap. Measurements and identification of modal pressure fields can be performed at a test rig without rotating components. Modal pressure fields can be described as acoustical resonances of a cavity bounded by the structures surfaces. An extension of Helmholtz-equation -the eigenvalue form of the acoustical wave equation- is formulated. It includes the influence of the fluid particles' vibration on the mode shape of the pressure field. Pressure modes in the cavity can be calculated using Finite Element Method. The results of numerical calculations show good accordance with the identified mode shapes based on measurement data. The coefficients of the modified wave equation and the necessary boundary conditions derive from measurement data and elementary numerical flow calculations. Models of modal vibrations of the coupled system based on its components' mode shapes can be developed using FE-calculations of the structures and the pressure field. Excitation of the vibration derives from the pressure changes in the labyrinth chamber due to periodic variations of fluid flow in the air gap. Comparison of fluid work in the labyrinth with vibrational energies of the structures gives a criterion for computer simulations of the coupled system. Amplitudes of the structures and the frequency of the system can be calculated and validate the assumption of vibration-coupling by the pressure field and excitation by flow forces in the labyrinth. Vibrations of the coupled system can be described as critically stable states which are characterized by an equilibrium of fluid work and the structures' vibrational energies.