This article is the second part of a series presenting and modeling the hydrodynamics and specific power consumption in shaking flasks on rotary (orbital) shaking machines. In part I, a new method was introduced that enables the accurate determination of the specific power consumption in shaking flasks. The method was first applied to investigate unbaffled flasks with a nominal volume of ≤1 L at low viscosity. In part II, the results for the specific power consumption of unbaffled shaking flasks at elevated viscosities are investigated after varying shaking frequency, flask size, filling volume, and shaking diameter. The theory introduced in part I is extended to liquids of elevated viscosities using nondimensional equations. With these results, the specific power consumption in unbaffled shaking flasks can now be fully described. For the first time, the phenomenon of the liquid being “out of phase” is observed and described. This occurs at certain operating conditions and is characterized by an increasing amount of liquid not following the movement of the shaking table, thus reducing the specific power consumption. This, of course, has much relevance for practical work with microbial cultures. The phenomenon of being “out-of-phase” is described in the form of a newly defined nondimensional phase number (Ph) in analogy to a partially filled, rotating horizontal drum. The Ph can be used to determine reasonable operating conditions for shaking flask experiments when using viscous media, avoiding unfavorable “out-of-phase” operation. © 2000 John Wiley & Sons, Inc. Biotechnol Bioeng 68: 594–601, 2000.