Abstract It is a classic result in database theory that conjunctive query (CQ) answering, which is NP-complete in general, is feasible in polynomial time when restricted to acyclic queries. Subsequent results identified more general structural properties of CQs (like bounded treewidth) which ensure tractable query evaluation. In this paper, we lift these tractability results to knowledge bases formulated in the lightweight description logics DL-Lite and ELH. The proof exploits known properties of query matches in these logics and involves a querydependent modification of the data. To obtain a more practical approach, we propose a concrete polynomial-time algorithm for answering acyclic CQs based on rewriting queries into datalog programs. A preliminary evaluation suggests the interest of our approach for handling large acyclic CQs.