The fast foward radiative transfer model used for the AIRS climate products will be presented. This model concentrates on high accuracy rather than speed, but is sufficiently fast for 1-D var retrievals. In addition this algorithm allows variation of CO, CH4, and column CO2. A simple algorithm to account for thin cirrus clouds has recently been added to the forward model (but is not scheduled for operational use). A critical component of the foward model are accurate spectral response functions (SRFs). We will discuss the pre-launch measurements of the AIRS SRFs and their impact on the accuracy of the AIRS forward model.