"Reciprocal Frame" refers to a self-supporting grid structure used both for floor and roof. Using Finite Element Methods for non-linear solid mechanics and frictional-contact, this paper intends to analytically and numerically investigate the collapse behaviour of a reciprocal frame structure made of fibre-reinforced concrete. Considering a simple 3-beam structure, it has been investigated using a solid finite element model. Once defined the collapse behaviour of the simple structure, the analysis has been generalized using a concentrated plasticity finite element method. Results provided will be useful for studying generic reciprocal frame structures with several beams.