Conservatories at gardens by the bay in Singapore consist of Cool Dry and Cool Moist, which are intended for the display of plants that typically thrive separately in cool dry and cool moist climates. The envelope itself consists of a grid shell-arch steel structure with a double glazed skin that sits directly on the grid shell, and the arches are the main load-bearing components. This paper analyzed the stability of one single arch whose span is the longest one in the corresponding structure, including buckling analyses and non-linear full range analyses. It also carried out stability analyses on some arch segments. The results showed that the stability bearing capacity of single arches met requirements, while some arch segments didn’t. After using the stiffening ribs, the local stability reached its requirements.