There is disclosed herein a method and apparatus that use ultrasonic signals to measure rheological properties of a fluid flow such as, e.g., the consistency index K, the flow behavior index n′, the yield stress &tgr;0, or other parameters of any given model for shear rate dependent viscosity &eegr;. In one embodiment, the method includes: (a) transmitting an acoustic signal into the fluid flow; (b) receiving acoustic reflections from acoustic reflectors entrained in the fluid flow; (c) determining a Doppler shift of the acoustic reflections in a set of time windows corresponding to a set of desired sampling regions in the fluid flow; and (d) analyzing the Doppler shifts associated with the set of sampling regions to determine one or more rheological properties of the fluid flow. The frequency shift caused by motion of the fluid is proportional to the velocity of the fluid, and this allows the construction of a velocity profile of the fluid flow stream. The velocity profile can be normalized and “matched” to one of a family of velocity profile templates, and the rheological properties identified by the curve that matches best. Alternatively, the shear rate as a function of shear stress can be calculated from the measurements, and these values may be used to find each of the parameters directly. In one embodiment, the apparatus includes a transmitter, a receiver, and an electronic module. The transmitter transmits an acoustic signal into the fluid flow. The receiver receives reflections of the acoustic signal from entrained acoustic reflection sources in the fluid flow. The electronic module is coupled to the transmitter and receiver, and is configured to provide a pulsed high frequency signal to the transmitter and, responsive to the signal from the receiver, to determine a velocity vs. position profile of the fluid flow.