The time behaviour of solids during unsteady temperature conditions is cons
idered. The conditions for the initiation of failure of a solid are formula
ted in the form of conditions for the attainment of the threshold values of
stress and strain fields. The evolution of a cracked region through the bo
dy is considered. It is shown that the destruction process is divided into
two stages in some cases. At the first stage, when a threshold value is ach
ieved at some point or region of the body a jump-like extension of the regi
on occurs until a state of equilibrium within the region is attained. This
jump-like destruction can be considered as an instability process. Various
examples are presented relating to the destruction of brittle solids. The i
nfluences of plasticity and time-dependent characteristics is considered.