We present a theory of the statically broadened vibrational line shape of a molecule in liquid solution. In this limit of static broadening, the molecule vibrates in a static potential posed by fixed solvent molecules in a configuration chosen from the equilibrium distribution of fluid configurations. The line shape is calculated within the instantaneous normal mode approximation, in which the solute’s potential is approximated by a harmonic surface whose curvature agrees with that of the exact potential at the solute’s initial configuration. Within this approximation, the line shape is related to a configuration-averaged phonon Green’s function, which is calculated approximately with an analytical procedure. This theory represents a modification of our previous treatment of vibrational line shapes [J. Chem. Phys. 102, 2326 (1995)], in which the solvent dynamics were included. Comparison of the line shapes for static and dynamic solvents permits determination of the relative importance of static (inhomogeneous) and dynamic (homogeneous) contributions to line broadening. We carry out such comparisons for a harmonic diatomic in a Lennard-Jones solvent over a wide range of temperature and density.