In belief functions related fields, the distance measure is an important concept, which represents the degree of dissimilarity between bodies of evidence. Various distance measures of evidence have been proposed and widely used in diverse belief function related applications, especially in performance evaluation. Existing definitions of strict and nonstrict distance measures of evidence have their own pros and cons. In this paper, we propose two new strict distance measures of evidence (Euclidean and Chebyshev forms) between two basic belief assignments based on the Wasserstein distance between belief intervals of focal elements. Illustrative examples, simulations, applications, and related analyses are provided to show the rationality and efficiency of our proposed measures for distance of evidence. Index Terms-Belief interval, dissimilarity, distance of evidence, evidence theory, the theory of belief functions. I. INTRODUCTION T HE theory of belief functions, also called Dempster-Shafer evidence theory (DST) [1], is an important mathematical framework for uncertainty modeling and reasoning. It has been applied to information fusion [2], pattern recognition [3], [4], multiple-attribute decision making [5], fault diagnosis [6], etc. DST has some limitations (see [7]-[9] for discussions). Generalized or refined theories were proposed including transferable belief model [10] and Dezert-Smarandache theory [7], [11], etc. In DST, the basic belief assignment (BBA) is a common way for modeling (epistemic) uncertainty. The distance of evidence is a crucial metric for measuring the distance between Manuscript