In metal physics, the free-electron model and the related Fermi-Dirac distribution were usually utilized to investigate multi-physical properties of metals. However, they neglected the important mechanical-electric coupling (MEC), and therefore some longstanding physical problems such as the positive Seebeck coefficients of some monovalent metals and the physical origin of charge density wave (CDW) gap may be difficult to solve. In the work, the MEC in metals was investigated. The MEC may lead to a single-electron model which can offer a simple way of interpreting the electron heat capacity, the Pauli magnetic susceptibility, the electrical conductivity and the electron thermal conductivity of the metals. It may also indicate that the heavy-fermion characteristics of the heavy-fermion systems may originate from the physical picture that the electron chemical potential intersects the narrow conduction f-electron band and the correlation effects among heavy-fermions may be weak, as is in contrary to the conventional viewpoint. Furthermore, it was found that the MEC can not only give the right sign of Seebeck coefficients of the monovalent metals but also give the physical origin of the CDW gap, which are in agreement with experimental results. Overall, the MEC may be important for the metals and it should be taken into account seriously for investigating the multi-physical properties of the metals.