Equations are solved by a flexible and rapid-convergent method; capable of capturing all sets of boundary conditions. A reduced order model is constructed to minimize the degrees of freedom in the fluid solution. The final coupled field solution is significantly faster than other conventional solution algorithms. A unified solution is provided to study the stability of fluid loaded conical shells, for the first time in literature. Stability margins of conical/cylindrical shells are reported for all sets of structural boundary conditions. The compressibility is shown to have significant effects on the dynamic characteristics of conical/cylindrical shells.