A propagation loss study is presented to determine the attenuation of various building walls. An approximate model was developed for the propagation of a spherical electromagnetic wave through a building wall of known material properties. This model is based on the method of images and geometrical optics. This approximate model is shown to be in good agreement with measured results. This work is part of a feasibility study for a miniature microwave powered surveillance vehicle that would be capable of operating inside buildings. For this application, the reflection and attenuation (insertion loss) of a focused microwave beam by interior and exterior walls is of interest. The insertion loss measurements were taken over a frequency range of 2 to 6 GHz.