We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model anddeformed Skyrme-Hartree-Fock model.The common points and differences of both models are systematically comparedand discussed.Their consequences on the stability of superheavy nuclei are explored and explained.The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed.The spherical shell effect disappears in some casesdue to the appearance of deformation or superdeformation in the ground states of nuclei,where valence nucleons occupysignificantly the intruder levels of nuclei.It is shown for the first time that the significant occupation of valence nucleonson the intruder states plays an important role for the ground state properties of superheavy nuclei.Nuclei are stable inthe deformed or superdeformed configurations.We further point out that one cannot obtain the octupole deformationof even-even nuclei in the present relativistic mean-field model with the σ,ωand ρ mesons because there is no parity-violating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativisticmean-field model. We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and formed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. The consequences on the stability of superheavy nuclei are explored and explained The theoretical results are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached. Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some casesdue to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupys ignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of valence nucleonson the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable inthe deformed or superdeformed configurations.We further point out tha t one can not obtain the octupole deformationof even-even nuclei in the present relativistic mean-field model with the σ, ωand p mesons because there is no parity-violating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativisticmean-field model.