Based on the mathematical apparatus of nonlocal hydrodynamics developed in Part 1 of the present paper, a specific problem of nonstationary motion of a flat plate in an incompressible liquid (the generalized Rayleigh problem) is solved. The solutions obtained are used to describe nonuniform motion of a viscous structural medium. It is demonstrated that in the case where the structural elements of the medium move with acceleration relative to each other, the kinematics of the flow on the mesoscale level (0.1-10 pm) is a vortex one. In this case, the scale of rotational cells is directly proportional to the difference between accelerations of neighboring mesovolumes. If the motion of mesovolumes is characterized only by the difference between their velocities, its character is a purely shear one. These results agree well with the experimental data on high-speed deformation of materials presented in this work. ©2000 Plenum Publishing Corporation.