1. A numerical study of composite spherical glass shells with separable sliding joints involving two types of annular steel frame with a flat joint has been used to completely characterize the overall stress state and the stress concentration zone. The boundary conditions adopted for models correspond entirely with those encountered in practice. 2. A new, efficient, separable joint for a composite glass spherical shell has been created. The proposed joint with an annular frame of selected shape and dimensions has promise, and it is recommended for use in similar structures. The joint devised may be applied in the two forms considered above. 3. Carrying capacity, endurance, and efficiency of brittle nonmetallic shells with a separable joint depend on the level of stress state disorder in the joint area. On the basis of analyzing the structural stress state in the joint area composite glass shells may be created in which it is possible to realize the high material strength obtained in uniaxial compression on test specimens. 2. The proposed joint may be improved by highly accurate assembly of the parts in the joint, and this is provided by reducing tolerances for mechanical treatment of the glass element in the joint section and local strengthening of the machined area by chemical etching in acid solution. 5. Since the proposed separable-joint construction does not provide hermeticity of the composite shell for the whole period of operation, it must be provided by special measures devised for each specific case.