A hydro-thermo-mechanical model is presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air

liquid water

and solid skeleton of concrete. Mass conservation equations

linear momentum conservation equation

and energy conservation equation are derived on the basis of the macroscopic Navier-Stokes equations for a general continuum

along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables are given with existing data from references. Specifications of the constitutive relations are made for the kinetic variables and their conjugate forces. Consequently a set of governing partial differential equations are obtained.