The paper investigates the mechanism of instability of deepwater risers fitted with fairings and presents an analytical model to predict the instability onset conditions. The simplified case of a two-dimensional (2D) problem was considered. The governing equations were derived, and the hydrodynamic forces were calculated and the effect of motion in these forces was taken into consideration. The final equations were linearised and an eigenvalue analysis was employed to systematically examine the stability with the emphasis on identifying the critical current speed for a given system. This model was validated against the available test results and showed a good agreement. A parametric study was also carried out. It showed the significant role of the hydrodynamic coefficients as well as mass distribution in the stability of the system.