A model for the numerical analysis of hygro-thermal and mechanical behaviour of concrete at high temperatures including transport, reaction and deformation processes is presented. For the description of transport and material behaviour the model comprises the balance equations for mass and enthalpy and the constitutive equations for concrete at high temperatures. The degradation of the cement minerals C-S-H and portlandite is described by two chemical reactions. The consideration of thermo-chemical damage in the classical non-local damage theory is discussed. Finally, the finite element formulation for solving the coupled balance equations regarding the primary variables displacement, temperature and relative humidity is presented and numerical results of a 3-D frame corner are discussed.