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Iron and cobalt distannides \ce{MSn2} (M = Fe, Co) are regarded as a promising conversion-type anode material for lithium- and sodium-ion batteries, but their properties are not well understood. In this work, we report a first-principles study of alkali metal (A = Li, Na) substitutional effect on the structural, mechanical, lattice vibrational, electronic and defect properties of these distannides. Special attention is paid to systematic comparison between \ce{FeSn2} and \ce{CoSn2}. Our calculations reveal that M/A substitution induces a lattice expansion and decrease of elastic constants, which is more announced with Na substitution than Li, and moreover changes the elastic property of \ce{FeSn2} from ductile to brittle whereas preserves the ductility of \ce{CoSn2}. An imaginary phonon frequency mode appears only for \ce{FeSn2} and \ce{FeNaSn2}, and M/A substitution provokes a definite gap between high and low frequency regions. We perform a careful analysis of electronic density of states, band structures and Fermi surface, providing an insight into difference of electronic structures between \ce{FeSn2} and \ce{CoSn2}. With further calculation of defect formation energies and alkali ion diffusion barriers, we believe this work can be useful to design conversion-type anode materials for alkali-ion batteries.