A novel model of hygrotheimal performance of cement based building materials during their maturing, considering evolution of their strength properties and deformations (shrinkage and creep strains), described in terms of effective stress is briefly presented.Creep is described by means of the modified mieroprestress-solidification theory by Bazant et al., with some modifications to take into account the effects of temperature and relative humidity on the cement hydration.Shrinkage strains are modelled by using effective stresses in the form introduced by Gray and Schrefler, giving a good agreement with experimental data also for low values of relative humidity.Results of two numerical examples based on the real experimental tests are solved to validate the model.They demonstrate its possibilities to analyze both autogenous deformations in maturing cementitious materials, and creep and shrinkage phenomena, in building elements of different age, sealed or drying at various conditions.