To explore a possible mechanism of deep earthquakes, this paper analyz
es the unstable propagation of a stress-induced phase transition which
is initiated in a homogeneous stress field. This Stephen problem is f
ormulated as an initial-value problem for the phase boundary, and the
driving force of the boundary is computed by using the solution of the
boundary-value problem for a partially transformed material. The prop
agation of the phase transition under uniform pressure is numerically
simulated. It is shown that (1) under lower pressure, the transition i
s terminated at a certain size, but it can propagate unstably when an
initially transformed region is sufficiently large; and (2) when the p
ressure attains a critical value, the propagation becomes unstable, an
d goes in a particular direction depending on the initial shape. These
results confirm the possibility of the unstable propagation of phase
transition, and provide a theoretical basis for the hypothesis that th
e phase transition of a mantle material can trigger a deep earthquake.