In our age in which the use of electronic devices is expanding all over the world, their reliability and miniaturization have become very crucial. The thesis is based on the study of one of the most frequent failure mechanisms in semiconductor packages, the delamination of interface or the separation of two bonded materials, in order to improve their adhesion and a fortiori the reliability of microelectronic devices. It focuses on the metal (-oxide) / polymer interfaces because they cover 95% of all existing interfaces. Since several years, research activities at mesoscopic scale (1-10µm) have proved that the more roughened the surface of the interface, i.e., presenting sharp asperities, the better the adhesion between these two materials. Because roughness exhibits extremely complex shapes, it is difficult to find a description that can be used for reliability analysis of interfaces. In order to investigate quantitatively the effect of roughness variation on adhesion properties, studies have been carried out involving analytical fracture mechanics; then numerical studies were conducted with Finite Element Analysis. Both were done in a deterministic way by assuming an ideal profile which is repeated periodically. With the development of statistical and stochastic roughness representation on the one hand, and with the emergence of probabilistic fracture mechanics on the other, the present work adds a stochastic framework to the previous studies. In fact, one of the Stochastic Finite Element Methods, the Perturbation method is chosen for implementation, because it can investigate the effect of the geometric variations on the mechanical response such as displacement field. In addition, it can carry out at once what traditional Finite Element Analysis does with numerous simulations which require changing geometric parameters each time. This method is developed analytically, then numerically by implementing a module in a Finite Element package MSc. Marc/Mentat. In order to get acquainted and to validate the implementation, the Perturbation method is applied analytically and numerically to the 3 point bending test on a beam problem, because the input of the Perturbation method in terms of roughness parameters is still being studied. The capabilities and limitations of the implementation are outlined. Finally, recommendations for using the implementation and for furture work on roughness representation are discussed.