This paper deals with the flexural instability of flexible spinning cylinders partially filled with viscous fluid. Using the linearized Navier–Stokes equations for the incompressible flow, a two-dimensional model is developed for fluid motion. The resultant force exerted on the flexible cylinder wall as the result of the fluid motion is calculated as a function of lateral acceleration of the cylinder axis in the Laplace domain. Applying the Hamilton principle, the governing equations of flexural motion of the rotary flexible cylinder mounted on general viscoelastic supports are derived. Then combining the equations describing the fluid force on the flexible cylinder with the structural dynamics equations, the coupled-field governing equations of the system are obtained. A numerical technique is devised with the obtained model for stability analysis of the flexible cylinder and some examples are presented. The effect of material viscoelasticity and structural damping on the stability margins of the flexible cylinder is examined, and some parameter studies on the governing parameters of the critical spinning speed are carried out.