A predictive compressive strength model accounting for the type of cement, cement degree of hydration, aggregates type and gradation, mixtures proportion and air content was developed. This paper presents the formulation, implementation, calibration and validation of the proposed strength model for normal concrete. The theoretical formulation postulates that particles' interaction is governed by excess paste theory from which an average paste thickness model is developed to account for concrete mixture proportions and aggregate gradation. In addition, the model accounts for the cement compressive strength and aggregate to cement paste bond strength. An experimental programme, developed to evaluate the model, accounts for the following variables: water to cement ratio, water content, bulk volume and maximum size of coarse aggregate, and air content. The proposed model is found to accurately predict the strength of concrete mixtures at 3, 7, 28 and 191 days. The measured 3-day and 28-day strength range from 8·5 to 32·7 MPa and from 13·6 to 43·8 MPa, respectively. The corresponding standard error and correlation coefficient for the 3-day predictions are 2·1 MPa and 0·95, and 1·8 MPa and 0·96 for the 28-day predictions.