Fiber-reinforced composites, due to possibility of modifying the mechanical properties, take on the role of conventional materials and find their application primarily in the aviation and automotive industries. The mechanical properties of composites depend mainly on the heterogeneous structure, distribution and fraction of constituents, between which various damages can occur. To determine the mechanical properties, it is necessary to use advanced test methods that provide insight into the phenomena that occur within the test specimen during loading. Computed Tomography (CT) allows a three-dimensional view of the external and internal state of a scanned object without damaging it. Mechanical tests can be performed ex-situ or in-situ inside the CT scanner. In ex-situ testing, the sample is loaded outside the CT scanner and then the sample is scanned in the unloaded state. However, in in-situ testing, the sample is loaded and scanned at the same time. Although in-situ tests provide a more complete insight into changes within the sample compared to ex-situ tests, their implementation is more complex and requires the use of specific test devices that fit inside the CT scanner. For this reason, developed in-situ cyclic fatigue machine for the project FULLINSPECT, which deals with the observation of the initiation and propagation of cracks, and identification of mechanisms of fracture within the fiber-reinforced composites during cyclic loading. During the operation of such a fatigue machine, vibrations occur which can damage the rotary table of CT scanner or affect the quality of recorded 3D images. Hence, in this thesis, a simplified model of the fatigue machine was developed and the most conservative case of loading at the maximum displacement amplitude of the test specimen of 1 mm was studied. Using the finite element method, the main vibration shapes were determined and the forces acting on the rotary table of the tomograph in the frequency range from 0 to 100 Hz were calculated.