Abstract: An analytic model of acoustic streaming generated in two-dimensional thermoacoustic waveguides with slowly varying cross-section is developed for more general applications.The analytical solutions of acoustic streaming characteristics in the closed straight tube and the annular tube are given based on the model.The solution for the closed straight tube can be applied to the case with any transverse scale.The solution for the annular tube is obtained under the assumption that the width of the varying cross-section part is much larger than the viscous and thermal penetration depths.The effects of cross-section variation,time-averaged temperature distribution and components of sound field are reflected in the analytic solutions.The magnitude and distribution of acoustic streaming velocity vary with the characteristic scale of the waveguides.The analytic model of acoustic streaming can be applied in research under thermoacoustic and other physical backgrounds.