We describe the radiative transfer modeling developed for the High Resolution Dynamics Limb Sounder (HIRDLS) instrument on board the NASA EOS-Aura satellite. HIRDLS is a 21-channel broadband radiometer operating in the spectral region between 6 and 18 microns. It is designed to rapidly measure limb emission at tangent heights from the upper troposphere into the mesosphere on a global basis. Science products will include profiles of temperature and chemical constituents, aerosol estimates, the location of polar stratospheric clouds, and geopotential height gradients. We present the HIRDLS fast forward model, which must accurately and quickly estimate transmittances and channel radiances for use in the operational retrievals. The forward model uses a physically based approach that combines transmittance estimates from Curtis-Godson and Emissivity-Growth approximations with a statistical regression. Channel-dependent radiance accuracies for an eleven-member test ensemble are 0.5--1.0% or better, compared to a line-by-line reference, and satisfy the forward model design requirements. We also discuss the forward model hierarchy developed for HIRDLS which underlies the fast model and provides benchmark calculations, detailed spectroscopy, and access to the physics of the radiative transfer process for development work. Collectively, this framework provides an effective solution to the requirement for fast and accurate radiative transfer modeling for operational use.