The major concern in Shallow arches behavior under lateral loading is their instability at a critical load, which can make the structure to collapse or displace to another stable configuration, a phenomenon called snap through. By introduction of functionally graded materials in recent years, and incorporating them into this problem, interesting results can be obtained which can give structures with favorable stability properties. In this work, dynamic stability of the hinged-hinged functionally graded shallow arch under implusive loading is investigated. Material properties vary through the thickness by power law. Nonlinear governing equations are derived using Euler-Bernoulli beam assumption and equations of motion are expressed by a nonlinear differential-integral equation. The solution utilizes a Fourier form of response. The procedure of analysis of dynamic stability that is followed in this work uses the total energy of the system and the Lyapunov function in the phase space that consists of essentially three steps: First, one finds all the possible equilibrium configurations of the shallow arch. Next, the local dynamic stability of each of the equilibrium configurations is studied.. Last, when the preferred configuration from which a snap through may occur is locally stable and when there is at least one other locally stable equilibrium configuration, then we proceed to find a sufficient, condition for stability against snap through. The effect of gradation on stability and critical load of the arch is investigated in detail.