We introduce novel mathematical models and algorithms to generate (shortest or k different) explanations for biomedical queries, using answer set programming. We implement these algorithms and integrate them in BioQuery-ASP. We illustrate the usefulness of these methods with some complex biomedical queries related to drug discovery, over the biomedical knowledge resources PharmGKB, DrugBank, BioGRID, CTD, SIDER, Disease Ontology, and Orphadata.