Recently, new compounds Mn₂RuSn and Mn₂RuSi were synthesized and their crystal structures were studied by X-ray diffraction measurements. This measurement indicates that they have a Heusler-like cubic structure, but the details have been unclear so far. To clarify their atomic arrangement and magnetic order, we carried out first-principles total-energy calculations for several different atomic arrangements, together with ferrimagnetic and ferromagnetic ordering. The comparison among total energies indicates that the most stable structure is a ferrimagnetic Hg₂CuTi one in both Mn₂RuSn and Mn₂RuSi. We also found that the compound Mn₂RuSi with the Hg₂CuTi structure could be a half-metallic ferrimagnet.