The author deals with the characteristics of the propagation of the waves of mechanical stresses in a linear viscoelastic three-dimensional continuum. In this continuum there is a void in the form of a circkular cylinder. The wave motion is due to a load moving in the said void, its magnitude being variable in time. A number of new effects is shown originating as a result of the viscous character of the medium for various combinations of material constants, load frequency and the velocity of its motion.