Due to the complex stress state near the curvilinear edge of composite laminates, three-dimensional (3D) finite element analysis is usually applied even it is time consuming. In this paper, in order to save computer time and storage, an asymptotic analysis is employed to separate the 3D problem into two plane problems. One is an interior problem, the other is a boundary layer problem. The former is treated by classical lamination theory and is solved by a special boundary element, the latter is then solved by the finite element developed for the generalized plane deformation problems. When the ratio of laminate thickness to hole diameter is small, the solutions for the laminates containing a circular hole are in good agreement with those obtained by the 3D finite element method.