In this paper an elastic stability analysis has been developed for spherical shell segments with fixed or horizontally removable edges. The shells are subjected to external hydrostatic pressure or the combination load, namely, hydropressure and frictional resistance. And when these forces act nonconservatively on the surfaces of the shells. It is shown, the dynamic (flutter type) instabilities as well as static (divergence type) instabilities often take place. The authors consider that these analytical results give some contributions to the study of elastic shell stability.