•Fractal dimension of concrete does not influence its tensile mechanical behavior.•Elastic modulus increases with increasing coarse aggregate content.•Tensile strength decreases with increasing coarse aggregate content.•Strain at the maximum stress decreases with increasing coarse aggregate content. The coarse aggregate content and fractal dimension were used to describe the geometric form of concrete at the meso-level. After the simulation results were validated, several meso-models of concrete with various fractal dimensions and coarse aggregate content were simulated under tension using Random Fractal Modeling. With increasing coarse aggregate content, the elastic modulus increased, and the tensile strength and the strain corresponding to the maximum stress decreased. The fractal dimension did not obviously influence the tensile mechanical behavior. The comprehensive consideration of both fractal geometry and classical Euclidean geometry can aid in predicting the macroscopic behavior of concrete.