Precise calculations of the isotope shifts in berylliumlike thorium and uranium ions are presented.The main contributions to the field and mass shifts are calculated within the framework of the Dirac-Coulomb-Breit Hamiltonian employing the configuration-interaction Dirac-Fock-Sturm method. These calculations include the relativistic, electronelectron correlation, and Breit-interaction effects. The QED, nuclear deformation, and nuclear polarization corrections are also evaluated.