We propose a rheometry using ultrasonic velocity profiling (UVP) that visualizes and evaluates quantitatively opaque complex fluids in a cylindrical open vessel performing unsteady rotation. The methodology termed "ultrasonic spinning rheometry (USR)" is expected to provide details of various rheological properties. In our study of USR applications, an enhancement in measuring some rheological properties was achieved for three different non-Newtonian fluids. For quantitative evaluations, we focused on momentum propagation in unsteady shear flows from an oscillating cylindrical container. In such flows, this propagation is represented in the radial profiles of the phase lag of velocity fluctuations. The phase lag information is obtained by a discrete Fourier transform of the spatio-temporal velocity distributions measured using UVP and indicates that the phase lag changes substantially as rheological properties change in a test fluid. As the primary rheological property, a local effective viscosity that is representative of the Newtonian viscosity in the bulk of a measurement volume is determined using UVP. In addition, the shear stress distribution, yield stress, spatial viscosity profile, and shear modulus are obtained as secondary rheological properties. (C) 2017 The Society of Rheology.