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The effect of foundations types on the snap-through buckling of a shallow arch under a point load moving at a constant speed for quasi-static and dynamic loading is investigated. First, the static and dynamic snap-through buckling of a shallow arch resting on a two-parameter elastic foundation (Pasternak model) under a point load moving at a constant speed are studied. For quasi-static analysis, it is noted that the first four modes in the expansion are sufficient to predict the response of the arch. Second, the dynamic snap-through buckling of a negative shallow arch resting on a fluid layer foundation under a point downward load moving at a constant speed is analyzed. The deformation of the arch is expressed in Fourier series. Third, the static and dynamic snap-through buckling of a shallow arch resting on a nonlinear one-parameter foundation under a point load moving at a constant speed is studied. The deformation of the arch is expressed in Fourier series.