When casting concrete structures, one of the most important properties is the concrete strength development. The need of actions on site is different at various stages of hardening, from the fresh concrete to the hardened concrete. The paper defines a model analysing maturity and associated strength growth within three important time periods. The model can be applied separately within each of these periods depending on test data available.It is shown in the paper that the temperature plays an important role on the strength development of concrete structures. The hydration rate increases with increased temperatures, which can be described by maturity functions. If the concrete temperature remains high, strength reduction at later ages usually occurs compared to hardening at lower temperature, which may be denoted strength reduction at elevated temperatures or cross over effects. Both these phenomena have been implemented in the model for strength growth presented in the paper. The functionality of the model is demonstrated by evaluation of laboratory tests for five concrete mixes and two types of cement.