This paper provides a procedure for the simulation of radiances from the U. S. National Oceanic and Atmospheric Administration (NOAA) Cross-track Infrared Sounder (CrIS) Fourier Transform Spectrometer to include spectral ringing effects caused by the finite-band, non-flat instrument spectral response to incident radiation. A simulation using a line-by-line radiative transfer model is performed to illustrate the magnitude of the effect and to indicate which spectral channels are likely to be impacted. Comparisons with CrIS observations are made to show that for most channels this effect is negligibly small compared to errors in the radiative transfer calculations but for the longwave edge of the CrIS longwave band and a few other regions, the brightness temperature ringing is significant. While the ringing artifact described in this paper may appear to be removed when Hamming apodization is applied, as is done for the assimilation of CrIS data into Numerical Weather Prediction (NWP) models, it is still present, and its influence reappears if the spectral correlation induced by apodization is properly handled to preserve the information content that derives from high spectral resolution. Inclusion of the instrument responsivity in calculated spectra to properly mimic the observed spectra as defined here eliminates artifacts from this type of ringing. Users of CrIS radiances should consider whether this effect is important for their application.