X-ray computed tomography (CT) holds a critical role in current medical practice for the evaluation of patients, particularly in the emergency department and intensive care units. Expensive high resolution stationary scanners are available in radiology departments of most hospitals. In many situations however, a small, inexpensive, portable CT unit would be of significant value. Several mobile or miniature CT scanners are available, but none of these systems have the range, flexibility or overall physical characteristics of a truly portable device. The main challenge is the design of a geometry that optimally trades image quality for system size. The goal of this work has been to develop analysis tools to help simulate and evaluate novel system geometries. To test the tools we have developed, three geometries have been considered in the thesis, namely, parallel projections, clam-shell and parallel plate geometries. The parallel projections geometry is commonly used in reconstruction of images by filtered back projection technique. A clam-shell structure consists of two semi-cylindrical braces that fold together over the patient's body and connect at the top. A parallel plate structure uses two fixed flat or curved plates on either side of the patient's body and image from fixed sources/detectors that are gated on and off so as to step the X-ray field through the body. The parallel plate geometry has been found to be the least reliable of the three geometries investigated, with the parallel projections geometry being the most reliable. For the targeted application, the clam-shell geometry seems to be the solution with more chances to succeed in the short term. We implemented the Van Cittert iterative technique for the reconstruction of images from projections. The thesis discusses a number of variations on the algorithm, such as the use of the Conjugate Gradient Method, several choices for the initial guess, and the incorporation of a priori information to handle the reconstruction of images with metal inserts.