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First-order perturbation analysis has been performed to investigate the stability and the fastest growth mode of a biaxially strained epitaxial thin film surface by stress-induced surface diffusion. It is found that the normalized critical wavelength along one principal direction depends on the Poisson’s ratio of the film, and also the perturbed wavelength and stress level along the other principal direction. The fastest growth analysis shows that when the absolute value of the ratio of the two principal stresses deviates from unity, a gradual transition from nanoisland formation to nanowire formation occurs. The larger the deviation, the stronger the tendency for the formation of a nanowire; finite element simulations confirm the tendency.