Genome-wide association studies of gene expression traits and other cellular phenotypes have successfully identified links between genetic variation and biological processes. The majority of discoveries have uncovered cis-expression quantitative trait locus (eQTL) effects via mass univariate testing of SNPs against gene expression in single tissues. Here we present a Bayesian method for multiple-tissue experiments focusing on uncovering gene networks linked to genetic variation. Our method decomposes the 3D array (or tensor) of gene expression measurements into a set of latent components. We identify sparse gene networks that can then be tested for association against genetic variation across the genome. We apply our method to a data set of 845 individuals from the TwinsUK cohort with gene expression measured via RNA-seq analysis in adipose, lymphoblastoid cell lines (LCLs) and skin. We uncover several gene networks with a genetic basis and clear biological and statistical significance. Extensions of this approach will allow integration of different omics, environmental and phenotypic data sets.