Computed tomography (CT) is an invaluable diagnostic tool in current medical practice. Unfortunately, the radiation dose imparted during a CT scan can be significant. This thesis seeks to develop, verify, and validate appropriate computational methods for computing this dose accurately and efficiently. The components of the model are the nuclear data, transport methods, and computer codes. Monte Carlo transport methods are employed primarily for their ability to accurately capture most of the relevant physical phenomena. Deterministic transport methods are subsequently verified and validated. The work is divided into three stages: experimental, verification, and validation. The experimental stage involves gathering high-fidelity data to aid in the validation procedures. Multiple radiation detection devices are employed to give greater certainty to the results. In addition, an important task is gathering data using a geometrically simplified phantom which is easier to model than the detailed Rando phantom. Towards this end, a CTDI FDA phantom is imaged. Exposure and dose measurements were taken in air and in the phantom center and periphery. The second stage, verification, involves the testing of the deterministic model for correctness of the methodology and the physics data, i.e. cross section library. Primarily, there are a few key assumptions which must be tested. The first is the importance of the secondary electron transport. Using Monte Carlo methods, it is found that the transport is unimportant for the accurate computation of the dose deposition distribution given the relatively low energy photons produced by x-rays tubes employed in CT scan machines. This makes the deterministic transport calculations much simpler. Next, the discretization of space, energy, and angle in the deterministic model is examined to ensure sufficient refinement capable of delivering accurate results. The Monte Carlo method is an excellent complement to deterministic methods, serving as reference as though it were an actual experiment, thus allowing the testing of these issues in a straightforward and highly controlled manner. In each discretization, the deterministic model proved capable, although some flux spectrum results differed by fifteen percent or more, mostly a result of the multigroup cross section set. Finally, after ensuring that the deterministic model was functioning as expected, a comparison was made of the simulations to the experimentally measured data. This was the most difficult of the tasks, in great part because of the lack of precise knowledge of detailed information concerning some of the parameters comprising the experimental setup. However, much effort was placed into conforming the simulations to the experiment as closely as possible. The ratio of exposures in the CTDI FDA phantom periphery-to-center is computed to within experimental uncertainty of about ten percent, while the absolute computed exposures have greater errors. The absolute exposures differed from the measured values by less than 35 percent.