The influences of the swirl (the fluid rotation) and the steady viscous forces of an annular flow on instability mechanisms of an outer functionally graded materials (FGMs) cylindrical micro shell are investigated. The annular flow passes the annulus between the inner micro shell and outer micro shell. The inviscid fluid-elastic forces related to the shell vibration are modeled in the frame of potential flow theory. The steady viscous forces induced by the fluid viscosity are obtained by using the time-averaged Navier-Stokes equations and then are coupled into the shell model in the form of initial loadings. The pre-loaded shell model is developed by means of the Hamilton's principle in conjunction with the modified couple stress theory. The pre-loaded shell motion equations are described based on the Flügge's thin shell theory. Afterwards, the zero-level contour method and the Galekin's method are employed to solve the problem. A parameter study and numerical comparisons are performed to evaluate the influences of all terms of inviscid fluid-elastic forces on the instability character of micro shell. Especially, the swirl effects are discussed fully. The results display different instability mechanisms of the fluid-micro shell system controlled by the swirl or/and the axial flow velocity. Eventually the fluid viscosity effects are given.