This thesis presents a model for the computer graphic synthesis of interactive fires. The term interactive is used to highlight two features of the proposed model absent from previous fire models: first, the fires interact with their environment like real fires by spreading over, charring, and lighting the objects which dictate the shapes and colors of the flames themselves. Second, useful forms of control are provided without a severe computational load to allow the user to interact with the model in the shaping of the final synthesis. Four constraints on model selection are identified in hopes of insuring these two forms of interactivity: the model must be convincing, controllable, contemporary, and computable. Convincing means that the synthetic fires visually mimic real fires in shape, color, and motion. Controllable means that the parameters of the synthesis are adjustable with appropriate physical, semantic, and other ``knobs.'' Contemporary means that the model is based on today's graphics paradigm and requires no new modeling, animating, or rendering techniques. Computable means that results render at rate which allowing for real-time interaction with the model. These four C's create the perspective with which background work is reviewed and the actual fire model derived. The model meets the four criteria by combining a perceptually-motivated, particle system flame model with a physically-based flame spread model. Both are presented in detail. Videotaped examples of synthetic results are available from the author.