The linear stability criterion proposed generalizes to continua earlier results obtained for the viscoplastic Shanley column. A sufficient condition for instability is marked by the change of sign of the real part of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the first bifurcation of a strain-rate-independent solid obtained in the limit of inviscid plastic flow.