Abstract <p>It is proposed to bury highly radioactive waste from nuclear power in deep mine or borehole storage facilities. The migration of actinides (²⁴¹Am and ²⁴⁴Cm) and fission isotopes (¹³⁷Cs and ⁹⁰Sr) from the repository with several horizontal boreholes was predicted by mathematical modeling. The radionuclide concentrations in near-surface waters were calculated as a function of the number, depth, and spacing between boreholes, the permeability of the surrounding rocks, and the time of waste storage prior to disposal. The advantage of horizontal boreholes over vertical ones is the low groundwater convection due to heat generation by the waste. With the same thickness of the rocks separating the waste from the surface, the temperature in the near field of a horizontal borehole is lower than in the case of a vertical borehole; for this reason, the intensity of radionuclide leaching from the glass matrix by water is also lower.</p>