Abstract Cancer drug sensitivity screens combined with multi-omics characterisation of the cancer cells have become an important tool to determine the optimal treatment for each patient. We propose a multivariate Bayesian structured variable selection model for sparse identification of multi-omics features associated with multiple correlated drug responses. Our model uses known structure between drugs and their targeted genes via a Markov random field (MRF) prior in sparse seemingly unrelated regression. The use of MRF prior can improve the model performance compared to other common priors. The proposed model is applied to the Genomics of Drug Sensitivity in Cancer data.