A scanning and imaging system utilizing 10 GHZ microwave beams for the detection of soft tissue tumors is proposed. Detection of such tumors is based on the fact that the micro-wave attenuation coefficient in muscle tissue is a factor of 10 greater than in fat. Thus a tomographic image computed from the transmission of a beam of microwaves scanned in a planar CT type raster through a body section should very easily identify areas of fatty tissue and muscle tissue on the order of 0.5 cm or possibly smaller. Since ionizing radiation is not used, this non-carcinogenic microwave technique is of particular interest for surveying and detecting tumors of the breast which are primarily muscle-like tissue in a fatty parenchema. The greatest risk results from the production of heat in the scanned tissue by the microwave beam, but it is shown to be negligible for the proposed scanner. An overall scanner design is discussed.