► Development of a cyclic sinh unified viscoplasticity constitutive model. ► Model applied to P91 steel under high temperature, cyclic loading conditions. ► Novel calibration technique for the identification of the viscoplastic parameters. ► sinh model allows the strain rate effect of 9Cr steels to be modelled accurately. An improved unified cyclic viscoplastic material model for high temperature fatigue of P91 steel is presented. The primary enhancement over existing models is in relation to strain-rate independence of parameters, for accurate interpolation and extrapolation across a range of strain-rates and stress regimes, as relevant to flexible operation of high temperature power generation plant. The model combines a hyperbolic sine constitutive equation with anisothermal cyclic evolution of isotropic and kinematic hardening variables. The material model is developed from a thermodynamic framework and is implemented in multi-axial form within a user material subroutine. The user material subroutine is calibrated and validated for P91 steel across a range of cyclic (isothermal fatigue and thermo-mechanical fatigue) and non-cyclic high temperature loading conditions. A novel method for the identification of the cyclic viscoplastic material parameters is also presented.