A multivariate two-sample testing problem is one of the most important topics in nonparametric statistics. One of the multivariate two-sample testing problems based on the Jurečková–Kalina ranks of distance is discussed in this article. Further, a multivariate Wilcoxon-type test is proposed for testing the equality of two continuous distribution functions. Simulations are used to investigate the power of this test for the two-sided alternative with various population distributions. The results show that the proposed test statistic is more suitable than various existing statistics for testing a shift in the locationt and location-scale parameters.