At early-age, hydration of cement leads to a reduction of volume (caused by the Le Chatelier contraction) which induces autogeneous shrinkage. Besides, hydration is an exothermic reaction and an increase of temperature occurs (followed by a decrease). As autogeneous shrinkage arises only in cement paste and as coefficient of thermal expansion may be different between cement paste and aggregates, strains incompatibilities lead to an internal self-equilibrated state of stress. Depending especially on the concrete mix, initial cracking may occur at the cement paste scale leading to a modification of the global concrete behavior. In this contribution, finite element simulations using a mesoscopic mesh are performed to access to the internal stresses and damage state due to the hydration process. Calculations take into account the autogenous shrinkage of the cement paste and the differential thermal behavior between cement paste and aggregates. Influence of basic creep strains, thermal boundary conditions and concrete mix (by a simplified approach) are studied showing that, for an ordinary concrete, hydration lead to a slight reduction of 'elastic' stiffness and tensile strength when creep is taken into account. On contrary on a high performance concrete, a significant reduction of the 'elastic' stiffness and tensile strength is expected (with respect to the potential tensile strength) even if the creep is taken into account.