Cylindrical shells are one of the most important structures that can be applied to engineering sciences due to their unique mechanical properties and also the problems of Fluid-Solid interaction are one of the most important structural issues. They are widely used in floats and bridges and reservoirs. As a result, the instability of these issues is very important. In this study, the vibrations of a FG cylindrical shell containing fluid with axial and rotary flow are investigated. Initially, the cylindrical shell equations based on the Donnell theory of thin shells, and then the vibrational equations of the structure by the Hamilton principle are developed respectively. The pressure generated by the fluid in the Hamilton equation is also obtained by the potential flow theory and the Bernoulli equation. Finally, with respect to the problem equations following the choice of the appropriate response function, the eigenvalue problem is obtained and the values ​​of the structure frequencies for different axial and rotational speeds is obtained. Also, frequencies of cylindrical shell filled with quiescent fluid in different modes are investigated and the effect of the power-law index of FG materials on the frequency of the structure with axial flow is shown.