For the modeling of infrared spectra it is a common approach to use a dielectric function that treats the vibrational modes as damped harmonic oscillators. This model was found to be rather crude for some applications to amorphous solids. A dielectric function model yielding a Gaussian shape of the absorption lines and satisfying Kramers–Kronig relations is suggested. The model function is constructed by a convolution of a Gaussian function with the dielectric function of the damped harmonic oscillator model. An analytical solution of this integral is given. It is demonstrated that this model describes the spectra of thermally grown ultrathin (1.3 nm) silicon oxide films, plasma‐deposited silicon films, plasma‐deposited silicon nitride films, and amorphous aluminum oxide films very well. The physical motivation of the dielectric function model suggested is the randomness of the vibrational frequencies in an amorphous structure.