The show that yielding in elastic plastic materials creates residual s
tresses when local disorder is present. The intensity of these stresse
s grows with the external stress and degree of initial disorder. The o
ne-dimensional model we employ also yields a discontinuous transition
to perfect plasticity when the lateral stress transfer approaches zero
. In the limit of vanishing but positive coupling we obtain the same c
ritical value of stress or surface energy, as reported earlier for the
two-dimensional case corresponding to the (1 + 1)-D minimal-interface
problem.