This master's thesis focuses on the analysis of the non-linear instability of flutter type and creating the reduction methodology of a complex FEM model into a more simple model. In the theoretical section, the introduction to the flutter problem is described with the introduction of parameters with the most significant impact on the critical flutter speed, followed by the description of simple methods of flutter analysis, accompanied by the methods of determining the critical flutter speed. The next section describes the simulation of the flutter instability on the model with two degrees of freedom, with the proper instability analyses and determining the critical flutter speed. This section is followed by the section describing the FEM model simplification using the modal reduction and by creating state-space model on which the stability of this system is observed, excited with the aerodynamic excitation introduced in the two degrees of freedom model, and subsequently, a flutter simulation in the time-domain is performed. Computational cost reduction of the model reduction is presented on the sensitivity analysis of each structure parameter and its impact on the critical flutter speed, with the investigation of the ones with the most significant impact, and the verification of these structure parameters' influence with the theoretical introduction at the beginning of this thesis.