Basic creep plays an important role in assessing the risk of early-age cracking in massive structures. In recent decades, several models have been developed to characterize how the hydration process impacts the development of basic creep. This study investigates the basic creep of various concrete mixes across different ages at loading. The analysis focuses on the very early stages (less than 24 hours) and early stages (less than 28 days) of concrete development. It is shown that a logarithmic expression that contains two parameters describing the material can accurately model basic creep from a very early age. One parameter relates to the creep amplitude and depends solely on the composition of the concrete. The other relates to the kinetics of creep and depends on the age of the material at loading and the nature of the concrete mixture. The logarithmic expression corresponds to a rheological model consisting of a single dashpot wherein viscosity exhibits a linear evolution over time. The model offers the advantage of eliminating the need to store the entire stress history for computing the stress resulting from the restriction of the free deformation. This approach significantly reduces computation time. A power-law correlation is also observed between the material aging parameter and the degree of hydration. This relationship depends on the composition. At least two compressive creep tests performed at two different degrees of hydration are needed to calibrate the material parameters and consider the effect of aging on basic creep compliance.