For guidance for developing Fe/Co-Sn-based anode materials for lithium-ion batteries, the mechanical, thermodynamic and electronic properties of FeSn5 and CoSn5 intermetallic phases under pressures ranging from 0 to 30 GPa have been investigated systematically using first-principles total-energy calculations within the framework of the generalized gradient approximation. The pressure was found to have significant effects on the mechanical, thermodynamic and electronic properties of these compounds. In the selected pressure range, CoSn5 has a more negative formation enthalpy than FeSn5. Based on the calculated elastic constants, the bulk modulus, shear modulus, and Young’s modulus were determined via the Viogt-Reuss-Hill averaging scheme. The variations of specific heats at constant volume for FeSn5 and CoSn5 in a wide pressure (0 - 30 GPa) and temperature (0 - 1000 K) range are also predicted from phonon density of states calculation. The calculated results suggested that both FeSn5 and CoSn5 are mechanically stable at pressure from 0 to 30 GPa. FeSn5 is dynamically stable at pressure up to, 30 GPa, at least, however, CoSn5 is dynamically stable no higher than 15 GPa.