In this paper, we present a new method to insert open surfaces into an existing tetrahedral mesh generated by the meccano method. The surfaces must be totally immersed in the mesh and must not intersect between them. The strategy includes a mesh re¿nement to obtain an initial approximation of each surface capturing its geometric features, the projection of the nodes from the approximation onto the actual surface, and the mesh optimization. The proposed method provides a high-quality conformal mesh with interpolations of the inserted surfaces. These approximations are suitable for operations where roughness is a major problem and a smoother solution is required, such as the estimation of normal vectors or the imposition of Neumann conditions.