Synthetic aperture radar (SAR) is a remote sensing technology for imaging areas of the earth's surface. SAR has been successfully used for monitoring characteristics of the natural environment such as land cover type and tree density. With the advent of higher resolution sensors, it is now theoretically possible to extract information about individual structures such as buildings from SAR imagery. This information could be used for disaster response and security-related intelligence. SAR has an advantage over other remote sensing technologies for these applications because SAR data can be collected during the night and in rainy or cloudy conditions. This research presents a model-based method for extracting information about a building -- its height and roof slope -- from a single SAR image. Other methods require multiple images or ancillary data from specialized sensors, making them less practical. The model-based method uses simulation to match a hypothesized building to an observed SAR image. The degree to which a simulation matches the observed data is measured by mutual information. The success of this method depends on the accuracy of the simulation and on the reliability of the mutual information similarity measure. Electromagnetic theory was applied to relate a building's physical characteristics to the features present in a SAR image. This understanding was used to quantify the precision of building information contained in SAR data, and to identify the inputs needed for accurate simulation. A new SAR simulation technique was developed to meet the accuracy and efficiency requirements of model-based information extraction. Mutual information, a concept from information theory, has become a standard for measuring the similarity between medical images. Its performance in the context of matching a simulation image to a SAR image was evaluated in this research, and it was found to perform well under certain conditions. The factors that affect its performance, and the model-based method overall, were found to include the size of the building and its orientation. Further refinements that expand the range of operational conditions for the method would lead to a practical tool for collecting information about buildings using SAR technology. This research was performed using SAR data from MIT-Lincoln Laboratory.