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.