An evaluation of the lateral spread that the proton beams undergo during their interactions with a water phantom has been performed. We calculated and evaluated the dose distribution spatially deposed of protons acceleration up to energies between 70 and 215 MeV using a voxelized water phantom as a 3D detector. A 0.1 mm3 size precision voxel was used to detect and calculate the deposed energy and dose in any area of the water phantom using the GEANT4 platform based on the Monte-Carlo Method simulation. We find that, regardless of the initial proton energy, the lateral spread follows a parabolic pattern as a function of depth, and the ratio of the radius at the Bragg peak to the depth of the Bragg peak is around 2.8%. A good agreement has been found compared to other analytical models, simulation methods, and especially to experimental data.