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This paper presents a stability-based analysis of amplification factors obtained using Fourier or von-Neumann method for the finite element formulation of shallow water equations. A Galerkin finite element model is developed for two-dimensional shallow water equations to obtain linearized form of the error equations. Fourier analysis is performed at finite element and node levels to propose time-step criteria for consistent methods using explicit, semi-implicit, and implicit schemes. The amplitude behavior as a function of the Courant and wave numbers is analyzed for square elements for two-dimensional field solution at each computational grid node.