  We use the ideas of Adly-Attoych-Cabot [Adv. Mech. Math., 12, Springer, 2006]
on finite-time stabilization of dry friction oscillators to establish a theorem
on finite-time stabilization of differential inclusions with a moving
polyhedral constraint (known as polyhedral sweeping processes) of the form
$C+c(t).$ We then employ the ideas of Moreau [New variational techniques in
mathematical physics, CIME, 1973] to apply our theorem to a system of
elastoplastic springs with a displacement-controlled loading. We show that
verifying the condition of the theorem ultimately leads to the following two
problems: (i) identifying the active vertex ``A'' or the active face ``A'' of
the polyhedron that the vector $c'(t)$ points at; (ii) computing the distance
from $c'(t)$ to the normal cone to the polyhedron at ``A''. We provide a
computational guide to implement steps (i)-(ii) in the case of an arbitrary
elastoplastic system and apply the guide to a particular example. Due to the
simplicity of the particular example, we can solve (i)-(ii) by the methods of
linear algebra and minor combinatorics.
