A novel reduced order formulation is proposed for the vibration analysis of conical shells containing stationary fluid. Hamiltonian approach is followed to obtain the governing equations of motion for the structure. Utilizing the Navier-Stokes equations and simplifying for irrotational, compressible and inviscid assumptions, the final fluid equation is obtained. A general solution based on the Galerkin method is proposed for the conical shell in vacuum. Several boundary conditions are investigated to show the capability of the proposed solution. A novel reduced order formulation based on the finite element method is developed for solution of the fluid equation. Static condensation technique is also utilized to minimize the required number of degrees of freedom and speed up the solution. The main advantage of the current solution method is the use of minimal number of degrees of freedom yet giving highly accurate results. Effects of added mass, semi-vertex angle, boundary conditions and different fluid containments on the natural frequencies of the coupled-field problem are studied and some useful conclusions are drawn. (C) 2016 Elsevier Ltd. All rights reserved.