The effects of an adjacent fluid’s viscosity and density on the characteristics of torsional stress waves transmitted in a waveguide with a circular cross section are studied theoretically and experimentally. Expressions for the torsional wave speed, dispersion relations, and attenuation are obtained as functions of the adjacent fluid’s viscosity and density. The theoretical results are compared with experimental observations. It is demonstrated that a device similar to the one described herein can be used as a rugged, real-time, on-line sensor for measuring the viscosity of a fluid with a known density. Such a sensor can measure the viscosity of fluids with a density viscosity product(ρfμ)greater than100 kg2/m4 sto a precision of 1% or better.