Shell structures found in engineering applications generally possess regions which are geometrically discontinuous, such as folds, intersections and creases. Analysis of such shell structures is a complex task and special attention is required for the analysis of intersections, folds etc.. Reissner-Mindlin shell theory is generally adopted for the analysis of shell structures with geometric discontinuities. In the present study, a new approach which blends Kirchhoff-Love shell theory with continuum solid theory is being developed for the analysis shell structures with geometric discontinuities. Kirchhoff-Love shell theory is adopted for the smooth regions of the shell, whereas the regions of shell intersections and folds are modeled using continuum solid theory. The concept of combining two different kinematic theories is being carried within the framework of Isogeometric analysis by adopting NURBS (Non-Uniform Rational B-Splines) functions as the basis. The performance of the new approach is demonstrated on a set of benchmark problems. Keywords: Shells, Folds, Intersections, Isogeometric analysis, Kirchhoff-Love Shell theory.