We present the result of anab initio search for new Dirac materials among inverse perovskites. Our investigation is focused on the less studied class of lanthanide antiperovskites containing heavy f-electron elements in the cation position. Some of the studied compounds have not yet beensynthesized experimentally. Our computational approach is based on density functional theory calculations which account for spin-orbit interaction and strong correlations of the f-electron atoms.We find several promising candidates among lanthanide antiperovskites which host bulk Dirac statesclose to the Fermi level. Specifically, our calculations reveal massive three-dimensional Dirac statesin materials of the class A3BO, where A=Sm, Eu, Gd, Yb and B=Sn, Pb. In materials with finitemagnetic moment, such as Eu3BO (B=Sn, Pb), the degeneracy of the Dirac nodes is lifted, leadingto appearance of Weyl nodes.