When the spatial or spatio-temporal sample size is extremely large, as in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. We first investigate how univariate tapering affects asymptotic efficiency of the maximum likelihood estimator (MLE) under the fixed-domain asymptotic framework for Matérn model. Then the tapering technique is extended to multivariate case with proposed multivariate compactly supported covariance matrix functions. The asymptotic properties of multivariate tapering for estimation and prediction are explored by using a domain-increasing framework. The computational gain, comparable results in estimation and co-kriging are illustrated by simulation study and an application to a US precipitation dataset.