The new spectroscopic studies of the exotic nuclei stimulate a development of the nuclear models to describe properties of nuclei away from the stability lines. Making use of the finite rank separable approach for the quasiparticle random phase approximation enables one to perform nuclear structure calculations in very large configuration spaces. Using the Skyrme interactions, we study the properties of the vibrational excitations in the even-even nuclei. In this seminar we briefly describe our approach. As an illustration of the method, we demonstrate the results for the quadrupole excitations in nuclei around 132Sn. Also, we concentrate on the results obtained for the charge-exchange excitations. The effects of the tensor correlations on the strength distribution of Gamov-Teller resonances in 118,120Sn are discussed.