Abstarct: Shallow arches are important structural elements used in civil, mechanical and aerospace engineering as part of complex structures. The major concern in their 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. In this study, we investigate the static and dynamic critical forces of a shallow arc beam with an initial form of sinusoidal function and general supports (springs) under a fixed point load. The nonlinear relations governing the shallow arc beam are obtained by assuming the Euler-Bernoulli beam and its equation of motion is expressed using a nonlinear differential-integral equation and given a Fourier cosine response and a auxiliary polynomial function has been resolved. The approach taken to analyze this problem is to use the whole system energy and Calculus of variations and partial integration. Finally, the effect of different types of support on the critical force of the arc is compared.