A mathematical model using the beam-shell compound finite strip method is established to study the elastic stability analysis of multi-trough rectangle aqueducts. The impacts of the transverse stiffeners and crossbars for the model are taken into account. The principle of minimum potential energy is used to deduce the eigenvalue equation for elastic stability problems. To verify the accuracy and efficiency of the beam-shell compound finite strip method, the numerical solution of the stability analysis for an actual aqueduct is calculated through the established model and other FEM methods. The result of the stability analysis for an actual aqueduct shows that: the buckling coefficient is reduced as the water level increasing while buckling mode remaining constant; and prestressed load has a great impact on not only the buckling coefficient but also buckling mode.