A vortex-shedding flowmeter uses two flow obstacles to provide stable generation of vortices that are detected as they pass through an ultrasonic beam between two transducers. The deleterious effects of acoustic signals reflected from the obstacles are minimized both structurally and electronically. The shapes of the obstacles are selected to reflect incident acoustic signals away from the beam between the transducers. Ultrasonic signals are generated simultaneously by two phase-opposed transducers and are detected in a time-windowed fashion in which the time window excludes extraneous reflected signals that have a longer path length.