Numerous metalloporphyrin stacks have been synthesized and studied. Electronic interactions between constituent metalloporphyrins are able to determine the structures and properties of porphyrin arrays. In 2016, Co(II)-, Cu(II)-, Pt(II)-, and Zn(II)-porphyrins were shown to pack to form dimers as well as trimers. Porphyrin rings were found to strongly overlap with lateral shifts between ring centers. However, no binding energies and electronic structures of these stacks have been reported. We have performed first computational study of the dimers of Co(II)-, Cu(II)-, and Zn(II)-porphyrins, both in vacuum and in two implicit solvents. For all three stacks the configurations with strong overlap of the metalloporphyrin rings with lateral shifts between ring centers were found to be the global minimum structures, 1A for [ZnP]2 and 3A for [CuP]2 and [CoP]2. Also, open-shell singlets with the same energy or close-lying in energy were found for [CuP]2 and [CoP]2. The binding energies were calculated to be significant, from ca. -13 to -39 kcal/mol (gas phase, depending on the computational approach). The computational results showed quite good agreement with the experimental data. The dimers were found to be bound by strong bonding combinations of the monomer MOs which explained significant binding energies computed for the dimers. The shifted dimer configurations could be explained by the way how the monomer MOs preferably overlap.