This paper introduces a comparative study for the compressive strength of concrete by employing machine learning approaches such as Genetic Programming (GP) and Artificial Neural Network (ANN). The simulation of concrete strength is strongly needed to better understand its behaviours under different conditions and loads. Since many studies predict the comprehensive strength of conventional concrete from hardened characteristics, based on the data points gathered from different experimental tests, empirical models have been developed and verified in the past years. Proposed models are more reliable if the numbers of tests increase and their repeatability increase as well. However, these models are designed for a specific range of concrete strengths. On the other hand, numerical models are more reliable since they are devised based on theoretical rules which could consider behaviours of concrete under different loading paths. But, the validation of these models is made by different loading paths with different configurations that result in costly experiments and both models use only principal stresses and strains in their formulation. Employing machine learning approaches instead of traditional models makes it possible to develop a better understanding of the compressive strength of concrete. Hence, the focus of this paper is the application of machine learning process and their suitability to model concrete compressive strength compared with early models obtained from the literature and compared with some conventional approaches.