The Collar grid method and the virtual grid method are jointly used in the embedding technique to solve the problem of finding the interpolating cells among the internal and external boundary points near the joint regions. With different boundary planes generated along different fixed surfaces, the Collar grid obtained using the hyperbolic partial differential equations can ensure to generate high-quality grids and to provide real interpolating cells for the boundary points on the joint regions. The main purpose of the virtual grid is to convert a solid wall boundary condition into an interface condition while no fluid flow computations are conducted within the virtual grid. The computational results of several configurations show that the currently developed embedding technique with Collar grid and virtual grid can effectively treat the geometrical configuration and can more accurately predict the flow over complex configurations with intersecting surfaces.