In this paper, the concept of stochastic dominance is introduced to Dempster-Shafer theory of evidence and several kinds of evidential dominance are proposed. In Dempster-Shafer theory of evidence, the expected utility is obtained as an interval. The seven kinds of inequalities between intervals are defined. The relationships among these seven inequalities are investigated. Using these inequalities, seven kinds of evidential dominance are defined. A necessary and sufficient condition for each evidential dominance is discussed. The usefulness of each evidential dominance is examined by a numerical simulation.