Passive control devices are used in structures to dissipate seismic energy with a view to minimise damages to the major structural components. A relatively new device, yielding shear panel device (YSPD), to exploit the shear deformation of thin metal plates to absorb energy has recently been developed. YSPD is formed by welding a thin steel plate within a steel square hollow section (SHS) and its behaviour is determined by complex interactions among the thin diaphragm plate, the surrounding SHS and the boundary conditions. Available experimental results show that YSPD produces nonlinear pinching hysteretic force-displacement response when subjected to cyclic loading. This paper proposes a mathematical model to predict the hysteretic response using easily available parameters, i.e. the geometry of the YSPD and the properties of the material. Results obtained from the verified finite element (FE) models are used to calibrate the proposed models, which should facilitate the full scale modelling of building frames retrofitted with YSPD.