In this paper we study the dynamic behavior of a shallow arch under a point load Q traveling at a constant speed. Emphasis is placed on finding whether snap-through buckling will occur. In the quasi-static case when the moving speed is almost zero, there exists a critical load $Qcr$ in the sense that no static snap-through will occur as long as Q is smaller than $Qcr.$ In the dynamic case when the point load travels with a nonzero speed, the critical load $Qcrd$ is, in general, smaller than the static one. When Q is greater than $Qcrd,$ there exists a finite speed zone within which the arch runs the risk of dynamic snap-through either while the point load is still on the arch or after the point load leaves the arch. The boundary of this dangerous speed zone can be determined by a more conservative criterion, which employs the concept of total energy and critical energy barrier, to guarantee the safe passage of the point load. This criterion requires the numerical integration of the equations of motion only up to the instant when the point load reaches the other end of the arch.

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