Theoretical description of thermodynamic response of materials upon changing of environment conditions is necessary for numerical simulations of physical phenomena at high pressures and temperatures. For example, equation of state for rhenium in a broad region of phase diagram is needed for modeling of hydrodynamic processes of powerful interactions with the substance. Furthermore, the equation of state of this metal is of crucial interest in connection with determining of the pressure scale in high-pressure experiments with diamond anvil cells. In the present work, a semiempirical model of the thermodynamic potential Helmholtz free energy as a function of volume and temperature is developed for rhenium with taking into account melting and evaporation effects. Based on the model, multiphase equation of state is constructed, and calculation of parameters of phase diagrams for the metal at high pressures and temperatures is carried out. A critical comparison of calculated results with available data of static and dynamic experiments for rhenium is presented. The work is supported by the Russian Science Foundation (grant No. 19-19-00713).