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Elastic gridshells making use of a rapid construction process, in which the spatial geometry of the gridshell is obtained by bending an initially flat grid. This particular shaping process saves time during the erection of the structure, as the grid members must not be bent individually but the grid can be shaped as a whole. Moreover, the assembly of the connections between the superposed rod layers of the grid can be done on the ground on a flat geometry. Nevertheless, in order to introduce shear stiffness to the initially unstable grid lattice, an additional layer of beam elements or diagonal cables must be added. The assembling of this bracing layer is usually time-consuming and requires additional supplies such as cherry-pickers or movable scaffolds. In this manner one of the great advantages – the rapid deployability of elastic gridshells – is clearly reduced. In order to accelerate the construction process of deployable elastic gridshells, we propose to use covering textile membranes as stiffening and at the same time cladding surfaces. In this paper we explain the design space for the development of elastic shells mainly made of GFRP and the structural behaviour of an elastic hemispheric gridshell braced with a membrane layer. Different connection configurations between membrane and grid have been analysed in FE-simualtions and the results have been compared with the load bearing behavior of a physical Prototype. [ABSTRACT FROM AUTHOR]