© 2016 IOP Publishing Ltd.Although several theoretical works were performed to describe the high pressure behavior of typical cubic elastic constants of cubic diamond silicon (dc-Si), some of the obtained results of these studies still remain inadequate and disagree with the experimental findings. To get more satisfactory results, we have investigated the phase transition, elasticity and other relevant mechanical properties of dc-Si were under pressures up to 14 GPa by applying original form of modified embedded atom method type interatomic potential for the first time with geometry optimization calculations. Phase transition pressure from dc-Si to β-Sn phase was found to be as 13 GPa which agree well with experiments. As well, under pressure, typical cubic elastic constants mimic the increasing behavior of experimental data and removes the earlier theoretical conflicts, in particular for C44. Further, bulk, Young and shear moduli, longitudinal and shear wave velocities, structural stability and brittle (ductile) character of dc- Si were also investigated under pressure. Obtained data of these surveyed quantities for the ground state of dc-Si well compare the previous experiments and other theoretical findings.