A shell structure of glass combines a highly effective structural principle with a material of optimal permeability to light. A facetted shell structure has a piecewise plane geometry, and together the facets form an approximation to a curved surface. A distributed load on a plane-based facetted structure will locally cause bending moments in the loaded facets. The bending stresses are dependent on the stiffness of the joints. Approximate solutions are developed to estimate the magnitude of the bending stresses. A FE-model of a facetted glass shell structure is used to validate the expressions and to give more detailed information about the distribution of the bending stresses.