Computational techniques are discussed for predicting acoustically induced flow within ducts whose cross-sectional dimensions vary continuously with axial distance along the duct. A formulation is introduced in which both the acoustic pressure and the axial component of the fluid velocity are expanded in terms of the local cross-sectional modal eigenfunctions, these depending implicitly on axial distance. A variational principle is derived and used to derive a set of coupled ordinary differential equations for the modal coefficients. A theory is also developed for the excitation of the field within the duct when a plane wave is incident at the baffled open end of the duct, the other end being closed. A potential application is in the design of an acoustic sensor that makes use of microclectromechanical sensor (MEMS) technology.