Circumferential grooves in the casing of an axial compressor rotor or fan are known to be beneficial by extending the operating range of the machine. The goal of this paper is to analyze, if such grooves have a significant effect on the flutter stability, too. Generally, flutter should always be avoided as these self-excited blade vibrations can lead to high-cycle fatigue and therefore may damage the blades. In the present paper, the flutter behavior of a nominal fan is analyzed by performing a unidirectional Fluid-Structure-Interaction (FSI) simulation. To model the traveling wave arising during flutter, three different possibilities are available for computational fluid dynamics (CFD): the traveling wave mode method (TWM), the Fourier transformation method (FT) and the influence coefficient method (INFC). The TWM and INFC will be used within this investigation. At first, the computed flutter stability of the commercial CFD solver ANSYS CFX is compared to the results of the academic CFD solver TBLOCK. Therefore, a MATLAB code is introduced to be able to use the very efficient INFC method in combination with ANSYS CFX. The main part of this paper deals with the examination of three different circumferential grooves. Two of them had been optimized regarding aerodynamics and aeroacoustics in a joint research project and produce a minor change in flutter behavior. The third groove is of an arbitrary chosen design and it is discussed how its axial position has an impact on the vibration characteristic of the fan. All CFD simulations are conducted for two different operating points at 100% speed and the first two eigenmodes of the fan blade.