Nickel based super alloys are promising materials for high temperature structural applications because of their low density. The single grain super alloys are extremely creep resistant at high temperature, due to the fraction of Ni3Al based ’ precipitates coherent with a Ni based  matrix [1, 3]. The cuboids group together and form semi-coherent interfaces after a long annealing at high temperature. The ’ precipitate growths in nickel base super alloys often favor the parallelism of (111) planes between cubic dissimilar crystals [4]. In consequences, a hexagonal network of dislocations, that covers the hetero-interphase, is arranged by accommodation of the angular misfit between two semi coherent crystals ( ). In this work, the magnitude of the distortions is simulated as arising from a trigonal network of subsurface misfit dislocations partly dissociated in Shockley dislocations limiting intrinsic and /or extrinsic stacking faults. The results derived from a previous explicit formulation using double Fourier series [5]. Each harmonic term of the series depends on the anisotropic elastic constants and the thickness of each phase. The program built is in a double precision Fortran language and it shows the magnitude and the aspect of the distortions of the free surfaces when the dissociation change in the hetero-interphase. Also, the program has the advantage to fully apply to hetero-epitaxial systems, whatever is the thickness of the free surfaces.