The impact of the tensor force on the properties of finite nuclei is discussed by analyzing the spin-orbit splittings and the multipole giant resonances in finite nuclei. It is found that the tensor force do plays an important role in nuclear structure. The experimental isospin dependence of the spin-orbit splitting is very well depicted when the tensor force is included. The tensor force has a larger effect on the spin flip magnetic dipole states than on the natural parity isoscalar quadrupole(2+, 3-) states. By analyzing the modifications to the Hartree-Fock mean field induced by the tensor terms, and the specific features of the residual particle-hole tensor interaction, we find that the tensor force gives an attractive contribution to the particle-hole matrix elements. Meanwhile the Landau parameters of Skyrme interactions in the spin and spin-isospin channels are studied by using various Skyrme effective interactions with and without tensor correlations. The role of the tensor terms is examined on the stability conditions of the spin and spin-isospin modes in nuclear matter above saturation densities. We point out that the spin and/or the spin-isospin instabilities are realized in the nuclear matter at the critical density of about 2 times more than the saturation density for all the adopted parameter sets. The critical density is shown very much depending not only on the choice of the Skyrme parameter set, but also on the inclusion of the tensor terms.