Tomographic imaging has provided the medical profession with unprecedented three-dimensional views of the internal structure of the human body. Similar techniques can provide solar physicists with an equally spectacular view of the three-dimensional structure of the solar corona, providing a new tool for addressing the problems of coronal structure, energy balance, and evolution. For the reconstruction process, images of the solar corona observed from different angular positions within the ecliptic are needed, and these are not yet available. The purpose is to demonstrate the utility and the practicality of solar tomography with a series of computer simulations of the process, while exploring the sensitivity of the results to some of the parameters of the observing process, e.g., the number of observations, angular spacing, and signal to noise. The results show that tomography can be a powerful technique for determining the three-dimensional nature of active region magnetic fields, coronal loops, helmet streamers, coronal holes, and other structures in the corona.