Using response-linearized linear muffin-tin orbital method we have studied the electronic band structure,phonon spectra,electron-phonon coupling and superconductivity of the new superconductor CaAlSi with AlB_2-type structure.The following conclusions are drawn from our calculations.(1)If Al and Si atoms are assumed to be arranged along the c-axis in a long-range ordered(—Al—Al—Al— and —Si—Si—Si—)structure,one should obtain the ultrasoft B_ 1g phonon mode and hence very strong electron-phonon coupling in Ca...