In this paper the mathematical modelling of a mechanical system designed to control changes in the pressure of the working medium in aircraft engines and consisting of a pipeline and a pressure sensor is carried out. The pipeline is necessary to take the sensor to some distance from the engine in order to mitigate the impact of high temperatures and vibration accelerations on the sensitive element of the sensor, which is an elastic plate. The system takes into account the aerohydrodynamic and thermal effects of the working medium on the plate. Asymptotic equations of aerohydrodynamics in the models of compressible and incompressible medium are used to describe the working medium motion in the pipeline. Both linear and nonlinear models of a deformable solid body are proposed to describe the plate dynamics. When using the compressible medium model, the solution of the problem is reduced to the study of an equation with a deviating argument. To solve the problem using the incompressible medium model, Fourier and Galerkin methods are applied. As a result, for both models the solution of the problem is reduced to the study of ordinary differential equations relating the magnitude of pressure in the motor with the magnitude of deformation of the sensing element, which can be used to control the mode of operation of the motor. The solution of these equations is found with the developed software program using standard functions of Mathematica 12.0. The paper was presented at PhysCon2024.