A theory describing pulse Doppler ultrasound signals due to backscattering due to emboli in flowing blood is presented. From this theory, the minimum detectable size of a formed-element embolus can be established as a function of carrier frequency and vessel size. Emboli can be sized and characterized, based on the ratio of the amplitude of the Doppler signal during embolus passage through the sample volume to background bloodflow Doppler signal when no embolus is present. This ratio is defined as the "embolus to blood ratio" (EBR). Size estimation of emboli can be done by insonating an embolus with a single frequency and measuring the EBR, only if the embolus does not exceed a certain size, and if the vessel diameter and per cent hematocrit are known. Using two different frequencies, the vessel geometry (diameter and sample volume length) and per cent hematocrit can be eliminated from calculation of embolus size. Sources of uncertainty in the EBR and their effect on embolus size estimation are discussed. Discrimination between gas and formed-element emboli is described, given a detector with sufficient dynamic range, and use of three carrier frequencies. The theory presented here is in agreement with experimental findings of other investigators.