  We study a relaxed formulation of the quasistatic evolution problem in the
context of small strain associative elastoplasticity with softening. The
relaxation takes place in spaces of generalized Young measures. The notion of
solution is characterized by the following properties: global stability at each
time and energy balance on each time interval. An example developed in detail
compares the solutions obtained by this method with the ones provided by a
vanishing viscosity approximation, and shows that only the latter capture a
decreasing branch in the stress-strain response.
