In this paper, Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) is introduced. It is an extension of Multidimensional Recurrence Quantification Analysis (MdRQA), which allows to quantify the (auto-)recurrence properties of a single multidimensional time-series. MdCRQA extends MdRQA to bi-variate cases to allow for the quantification of the co-evolution of two multidimensional time-series. Moreover, it is shown how a Diagonal Cross-Recurrence Profile (DCRP) can be computed from the MdCRQA output that allows to capture time-lagged coupling between two multidimensional time-series. The core concepts of these analyses are described, as well as practical aspects of their application. In the supplementary materials to this paper, implementations of MdCRQA and the DCRP as MatLab- and R-functions are provided.