Overcoming the force of gravity is an important part of space travel and a significant obstacle preventing many seemingly reasonable space travel schemes to become practical. Science fiction writers like to imagine materials that may help to make space travel easier. Negative mass -- supposedly causing anti-gravity -- is one of the popular ideas in this regard. But can mass be negative? In this paper, we show that negative masses are not possible -- their existence would enable us to create energy out of nothing, which contradicts to the energy conservation law.