Human carcinomas are comprised of complex mixtures of tumor cells that are known to compete indirectly for nutrients and growth factors. Whether tumor cells could also compete directly, for example by elimination of rivals, is not known. Here we show that human cells can directly compete by a mechanism of engulfment called entosis. By entosis, cells are engulfed, or cannibalized while alive, and subsequently undergo cell death. We find that the identity of engulfing ("winner") and engulfed ("loser") cells is dictated by mechanical deformability controlled by RhoA and actomyosin, where tumor cells with high deformability preferentially engulf and outcompete neighboring cells with low deformability in heterogeneous populations. We further find that activated Kras and Rac signaling impart winner status to cells by downregulating contractile myosin, allowing for the internalization of neighboring cells that eventually undergo cell death. Finally, we compute the energy landscape of cell-in-cell formation, demonstrating that a mechanical differential between winner and loser cells is required for entosis to proceed. These data define a mechanism of competition in mammalian cells that occurs in human tumors.