The pressure-dependent energetic and mechanical stabilities of simple cubic carbon were studied using first-principles calculations. The enthalpies of graphite, diamond, BC8, and simple cubic carbon were calculated, and it was found that simple cubic carbon was the most energetically stable polytype above 2700 GPa. Elastic constants were calculated as a function of pressure. Simple cubic carbon was mechanically unstable below 400 GPa, but became mechanically stable above 400 GPa. Our calculated results also indicated that the bulk module of simple cubic carbon increased linearly with increasing pressure.