We describe an approach to absolute stellar calibration of broad and narrowband infrared filters based upon new models of Vega and Sirius due to Kurucz [private communication (1991)] and calculated by him, for the first time, with realistic stellar metallicities and a finely-gridded wavelength scale in the infrared. After normalizing the Vega model so that it matches Hayes' [Calibration of Fundamental Stellar Quantities, Proc. IAU Symposium No. Ill (1985)] weighted average of six monochromatic 5556A measurements we integrate the model through a variety of infrared filters using determinations of filter transmission profiles obtained at their actual operating temperature, and detailed model calculations for terrestrial atmospheric transmission. This provides in-band fluxes for Vega, which we define to be zero magnitude at all wavelengths shortward of 20 mum. We use existing infrared photometry differentially to establish an absolute scale for the new Sirius model. This yields an angular diameter within 1sigma of the mean determined interferometrically by Hanbury Brown et al. [MNRAS, 167, 121 (1974)]. For practical purposes, Sirius provides the absolute calibration beyond the 20 mum region because of Vega's dust shell. Isophotal wavelengths and monochromatic flux densities for both Vega and Sirius are tabulated. We attempt a comparison of our calibration figures for the IRAS wavebands with the process used to generate the original IRAS absolute calibration. A complete duplication of that process is not currently possible. Preliminary indications are that IRAS is too high by 2%, 6%, 3%, and 12% at 12, 25, 60, and 100 mum, respectively.