Snap-through is an instability phenomenon that occurs in arch and dome-shaped structures, wherein the structure has to move from a stable equilibrium state through an unstable path into another stable equilibrated configuration in a jumping action. In this study, a linear elastic isotropic low arch is considered as a structure with power-law variable thickness. The phenomenon is investigated by considering the equation of the deflection for the variable thickness arch, solving it with an elegant analytical technique, and finding the snap-through critical load from an extreme condition. The effect of power-law exponent and geometry of the arch centerline on critical load is investigated and the constant thickness case and a very rare case of power-law thickness variation found in literature are considered for verification.