We propose a practical and flexible solution to introduce skewness in multivariate symmetrical distributions. Applying this procedure to the multivariate Student density leads to a ``multivariate skew-Student" density, for which each marginal has a different asymmetry coefficient. Combined with a multivariate GARCH model, this new family of distributions is potentially useful for modelling stock returns, which are known to be conditionally heteroskedastic, fat-tailed, and often skew. In an application to the daily returns of the NASDAQ and the DAX, it is found that this density suits well the data and clearly outperforms its symmetric competitor.