The iterative process of design-analysis-redesign implies urgent requests of the integration of computer aided design (CAD) and computer aided engineering (CAE). In this paper, we present a numerical manifold method (NMM) based on CAD geometry: we can arrange mathematical meshes and set order of approximation functions according to the complexity degree of physical field distribution in CAE, which is more reasonable than isogeometric analysis (IGA) method. Through introducing automatic and fast cutting operations, we can realize direct modeling from CAD model to CAE model without modifications. Moreover, to solve the problem that curves on geometric boundaries are required to be discretized into line segments in present NMM, we put forward algorithms to cut the curves of geometric boundary with the lines of mesh boundary, hence preserving the shape of the geometric model in the procedures of CAE modeling and mesh refinement. Furthermore, as for the polynomial approximation functions usually used in NMM, we deduce analytical integral formula of “approximate” simplex with a curved edge and use it to obtain precise integral calculations of manifold elements with curved boundaries. Finally, we verify the feasibility of the method through an example of a circular hole in a plate. The research offers new thinking for the integration of CAD and CAE, and lays foundation for the automatic analysis from CAD models to CAE.