The paper presents the problem of unstable viscoplastic fluid flow between parallel planes, one of which is fixed, while the other one is put in motion from a standstill under the influence of constant force. Viscoplastic fluid flow develops gradually. The border of the flow is not known in advance and is to be determined in the process of solving the task. The force applied to the upper plate is chosen so as to cause the effect of sliding along the two plates in the course of time.
