Thin shallow arches may become unstable under transverse loading if the built-up internal compressive forces reach a limiting value beyond which the structure undergoes a sudden large displacement towards a new stable configuration. This phenomenon could be both desirable (in toggle switches) and disastrous (collapse of a dome or truss). Hence, the so-called snap- or limit-load analysis becomes important as to which factors influence it to give guidelines in designing structures to behave favorably. By the introduction of functionally graded materials (FGMs) in recent years, and incorporating them into this phenomenon, interesting results can be obtained which can give structures with favorable instability properties. In this work, a thin shallow arch with a modulus that can be varied along the thickness or the arch length or both is considered. Based on the governing equations of the deflected arch, the snap load is obtained in a mixed analytical-numerical approach and a parameter study of the critical load is carried out. Several verifying and interesting examples are presented.