Modelling the propagation of sound waves in the ocean is challenging because one must account for spatial variation in properties of the fluid and in the ocean geometry, as well as couple the fluid to a seabed that supports both shear and compressional waves. This article presents a f inite element based approach to obtaining the eigenmodes for an axial uniform ocean waveguide. Once these modes have been computed, an orthogonality relation is used to compute the sound pressure field for ranges of up to 5 km. This approach avoids the traditional heavy computational expenditure associated with the finite element method, at least for a uniform waveguide. Furthermore, the numerical approach properly accounts for the depth dependent properties of the ocean, and couples the ocean to a full elastodynamic representation of the seabed, which supports both shear and compressional waves. This permits the implementation of the physically correct transverse boundary conditions, as well as the addition of a perfectly matched layer to enforce the correct boundary conditions at infinite depth in the seabed.