An ultrasonic densitometer for measuring the density or a density related parameter of a fluid has at least one transducer assembly that transmits and receives torsional waves guided in an axially extending sensor that is at least partially immersed in the fluid. The sensor has a noncircular cross section, typically rectangular, with dimensions, aspect ratio, frequency and bandwidth selected to limit dispersion. This non-circularity creates an inverse and substantially linear relation between the density of the fluid and the velocity of the torsional wave in the sensor. To meet special requirements, the sensor can take a variety of forms including axially curved, axially profiled, segmented or longitudinally composite. This densitometer, alone or in combination with conventional auxiliary ultrasonic measuring systems, can measure fluid density, density profiles, liquid level, viscosity, mass flow rate, gas pressure, and boiling or condensation, including measurements of flowing fluids in small conduits.