We develop the free and open-source model Multi-tissue Splicing (MTSplice) to predict the effects of genetic variants on splicing of cassette exons in 56 human tissues. MTSplice combines MMSplice, which models constitutive regulatory sequences, with a new neural network that models tissue-specific regulatory sequences. MTSplice outperforms MMSplice on predicting tissue-specific variations associated with genetic variants in most tissues of the GTEx dataset, with largest improvements on brain tissues. Furthermore, MTSplice predicts that autism-associated de novo mutations are enriched for variants affecting splicing specifically in the brain. We foresee that MTSplice will aid interpreting variants associated with tissue-specific disorders.