Multivariate responses are commonly encountered in many applications with high dimensional input variables. Feature screening has been shown to be a very useful data analysis tool for high dimensional data. Since the sure independence screening paper by Fan and Lv (2008), many variable screening methods have been proposed and studied in the literature. Yet, the majority of the existing screening methods handle the classical univariate response data case and do not apply naturally to the multiple responses datasets. In this paper, we systematically study variable screening methods for multi-response data. First, we consider extensions of several popular screening methods to deal with multiple responses. Each of these methods has its own clear drawbacks. We then propose a new model-free screening method named multi-response rank canonical correlation screening (mRCC). It not only takes into account the dependence structure among the multivariate responses but also preserves nice properties of the rank correlation such as robustness and invariance under monotonic transformation. The sure screening property of mRCC is established under weak regular

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