An analytical rheological model capable of describing the loading speed dependent in-plane shear behaviour of a masonry multi-layer bed joint is presented in this paper. Such joints consist of a core soft layer protected by two thin extruded elastomer membranes, which in turn are placed in a bed mortar joint. The extruded elastomer membranes are employed to prevent and/or limit the deterioration of the core soft layer during the cyclic action observed in previous investigations. Joint behaviour is assumed to be linear elastic-perfectly viscoplastic and has been captured by a uniaxial model consisting of three elements: an elastic spring connected in series with the frictional slider and a dashpot (viscous damper). The rheological model is characterized by three material parameters that have been assessed from several series of monotonic and static-cyclic tests on small masonry specimens (triplets). In addition to these three parameters, the contraction of the thickness of multi-layer bed joint due to pre-compression has been considered too. Although model parameters are determined for the multi-layer bed joint with a rubber granulate core soft layer, the parameter space can be extended to the other types of core soft layer once the appropriate test data becomes available.