Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter μ. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter ε, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting ε = 0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (ε 1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter μ. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic). © 2012 Acoustical Society of America.