We report a new stress-induced kinetically driven morphological instab
ility for driven systems. The effect of stress on the interfacial mobi
lity couples to stress variations along a perturbed planar growth fron
t. Comparison of theory and experiment for solid phase epitaxy at a co
rrugated Si(001) interface, with no free parameters, indicates that th
e new mechanism is required to account for the observed growth of the
corrugation amplitude. This mechanism operates in conjunction with kno
wn diffusional and elastic strain energy-driven instabilities in deter
mining morphological evolution.