A novel hybrid finite element method (FEM) -uniform theory of diffraction (UTD) method for the analysis of radiating structures in the presence of electrically large objects is presented. The hybridization is done in a fully coupled way taking into account mutual interactions between the FEM and UTD regions. The UTD objects are modeled using non-uniform rational B-spline (NURBS) surfaces. Ray acceleration techniques and simple clustering strategies are used to speed up the computation time. Numerical results are presented showing the validity of the method.