A formulation, based on the semi-analytical finite element method, is proposed for elastic conical shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Finite element analysis of fluid-filled isotropic cylindrical shells with constrained viscoelastic damping, Computers & Structures 70 (1998) 363-376] while the fluid model is based on velocity potential formulation used by Jayaraj et al. [A semi-analytical coupled finite element formulation for composite shells conveying fluids, Journal of Sound and Vibration 258(2) (2002) 287-307]. Dynamic pressure acting on the walls is derived from Bernoulli's equation. By imposing the requirement that the normal component of velocity of the solid and fluid are equal leads to fluid-structure coupling. The computer code developed has been validated using results available in the literature for cylindrical shells conveying fluid. The study has been carried out for conical shells of different cone angles and for boundary condition like clamped-clamped, simply supported and clamped free. In general, instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency. Critical fluid velocities are lower than that of equivalent cylindrical shells. This result holds good for all boundary conditions. © 2007 Elsevier Ltd. All rights reserved.