A micro-mechanical scheme has been coupled to a hydration model in  so as to investigate the instantaneous mechanical properties of a concrete. That scheme is extended to aging linear viscoelasticity so as to estimate the basic creep of concrete. The compliances of the hydrate phases are set according to existing nanoindentation tests. Then, aging is induced by the progressive dissolution of the unhydrated particles and the precipitation of hydrates at the expense of the capillary porosity. Eventually, these new estimates are extensively compared to 380 published experimental results of basic creep tests gathered in the NU database, thus showing that the method is operational, versatile and reasonably accurate. Finally, accounting for the Young modulus at the time of loading by scaling the estimated strains proved a justified and efficient correction.