New model atmosphere calculations for very cool white dwarfs with mixed H/He and pure He compositions are presented. The hydrogen-rich models incorporate improved cross section calculations of the collision-induced absorption by molecular hydrogen due to collisions with H-2, H, and He. The effects associated with variations in the effective temperature (4000 less than or equal to T-eff less than or equal to 10,000 K), the surface gravity (7.5 less than or equal to log g less than or equal to 9.5), and the chemical composition [0 less than or equal to N(He)/N(H) less than or equal to 100] are investigated. Results from earlier calculations are confirmed qualitatively, but a more detailed comparison reveals large quantitative deviations. Cool white dwarfs with mixed H/He chemical compositions are shown to be easily recognizable from their predicted strong infrared flux deficiency. Pure helium model calculations are described as well. These include a modified version of the recently devloped equation of state of D. Saumon and G. Chabrier. Nonideal effects brought about by various equations of state are explored in detail. For the purpose of this analysis, a model of pressure ionization based on an accurate description of the interactions in a mostly atomic helium fluid is developed. The effects of pressure ionization are shown to be the most important issue in the model calculations. A critical discussion of previous generations of pure helium model calculations is presented. Finally, broadband color indices are provided for the complete model grid.