In the weak interacting limit, topological insulators (TIs) can be classified according to their band topology, and their physical properties can be analyzed perturbatively. However, in the strongly interacting systems, electron bands are not good starting points, and taking operations to the wavefunctions are not accessible neither. Usually, fixed-point wavefunctions can be obtained in the exactly solvable models, which are quite complicated and involved. One need to go beyond fixed-point wavefunctions in order to actually make the wavefunctions variational and operational. We tackle such challenges by introducing a framework that generate variational tensor (fPEPS) ansatz of ground state wavefunctions in the correlated insulating systems. Within this framework we can directly examine the classification and the edge properties of correlated topological insulators with given symmetry groups. In this talk, I will firstly discuss interacting quantum spin Hall states as an example to illustrate the basic ideas of our framework, and I will also examine its edge theory in the tensor representations. I will then discuss the cases of general TIs with any given symmetry groups.