Concrete is considered to be a composite material consisted of cement paste binder, some additives and plasticizers, and inclusions of gravel and chip. Concrete properties are changing continuously during the concrete curing process. Prediction of changes in strength and stiffness characteristics affects significantly the building construction process; thus, such prediction is very important. Concrete is treated as a three-periodic elastic medium with time-dependant stiffness characteristics. In this paper, the application of cell functions for prediction of concrete macro characteristics and their changes over the period of concrete strength development is investigated. The macro characteristics are calculated by integration of cell functions that are derived from solving a family of boundary value problems on periodic cell. It is shown that calculations of averaged modulus of elasticity and Poisson’s ratio for regular isotropic medium over a time period are in good agreement with well-known experimental dependencies.