Abstract : Electromagnetic diffraction is studied in many industrials domains. Some studies about small bodies face to the frequency, use numerical methods based on integral Maxwell equations : Methods of Moments and more recently Multipols Methods. In case of large bodies or at high frequency, these methods become quickly too expensive. The aim of this thesis is to bring an other approach that uses asymptotic expansions which allows to solve these problems thanks to a formulation based on the Geometrical Theory of Diffraction (GTD). The application of a boundary layer method to these problems for regular bodies close to the shadow boundary region and in the shadow region yields integral representations of the diffracted field involving Airy functions. The application of this method on elongated bodies involves bi-confluent Heun equation. As there is no analytic solutions for this Heun equation, solutions can be obtained by approximating this equation. The numerical results we obtained by implementation of theses formulations associated to a ray tracing algorithm are very good compared to integral methods results.