Inter-individual variation in gene expression levels can arise as an effect of variation in DNA markers. When associating multiple gene expression variables with multiple DNA marker variables, multivariate techniques, such as canonical correlation analysis, should be used to deal with the effect of co-regulating genes. We adapted the elastic net, a penalized approach proposed for variable selection in regression context, to canonical correlation analysis. The number of variables within each canonical component could be greatly reduced without too much loss of information, so the canonical components become easier to interpret. Another advantage is that it groups co-regulating genes, so that they end up in the same canonical components. Furthermore, our adaptation works well in situations where the number of variables greatly exceeds the number of subjects.