This paper presents the numerical modeling of plain concrete specimens subjected to uniaxial tensile stresses. The simulations are performed using a three-dimensional macroscopic probabilistic model for semi-explicit concrete cracking. As it is well known, concrete structures are largely sensible to the scale effects that can be attributed, among other reasons, to the heterogeneous nature of the material. The model used herein, which is developed in the framework of the finite element method, considers the material heterogeneity through the assumption that each finite element represents a volume of heterogeneous material, with mechanical properties of tensile strength and fracture energy being randomly distributed over the mesh according to the Weibull and lognormal distributions, respectively. The cracks are created with different energy dissipation according to an isotropic damage law. The results are obtained through Monte Carlo simulations using a parallelization strategy with OpenMp to allow feasible 3D simulations of real structures in a viable computational time. With the purpose of modeling the uniaxial tensile test and verifying the prediction of the scale effects, simulations of three prismatic plain concrete specimens with different sizes are performed.