This study concerns with the evolution of morphological patterns that often arise on the interface of bi-material, so called metal-precipitate phase, due to the instability of the interfaces. The instability leads to growth or retraction of small perturbation, which may determine the formation of a variety of morphological patterns initially arising on surfaces of growing precipitates at small length scales. To better understand the cause of different patterns on the bi-material interfaces, an analytical study of the stability of the precipitate-matrix interface is performed. First, a wavy interface perturbation is used to examine the spontaneous variations that occur at the precipitate-matrix interface. Then, the analysis utilises Cerruti?s solution to compute the perturbed stress field surrounding the interface. It is shown that a virtually flat interface subjected to tension is in general unstable. The amplitude of sinusoidal perturbations decays for short wave lengths and grow for longer wave lengths. Both a critical wave length for which the perturbation amplitude is unaffected and a specific ditto which obtain maximum perturbation growth rate are derived