Abstarct: The aim of this thesis is investigation the energy spectra and transition rates of even-even heavy nuclei. For this purpose, three symmetric models, E(5), X(5) and X(3), have been used. When the X(3) model was introduced (in 2006), its potential was considered as an infinite square well, its eigenvalues and eigenstates were determined and they compared with the experimental data. Then, in order to improve the theoretical results and gain the better agreement with the experimental data, the other potentials like Sextic were used. In this thesis, the X(3) model has been investigated with the harmonic oscillator energy dependent and modified Davidson potentials. In 2015, when the hybrid model was introduced, its β and γ dependent potentials were respectively considered as an infinite square well and harmonic oscillator. After, without changing the γ dependent potential, the β dependent one was considered as Davidson, but since the results of these two cases do not have good agreement with the experimental data of some nuclei, we proposed the Killingbeck potential. We obtained the relevant energy spectra and transition rates by applying the variation method and compared our results with both previous theoretical results and experimental data. We also introduced the combined model, investigated it with the Morse potential and compared the obtained results with both experimental data and the results of the E(5) model with Morse potential. Moreover, we studied the X(3) model in the presence of position dependent mass formalism with both the Coulomb-like and modified Davidson potentials. In addition to the different potentials, introducing the combined model and consideration the X(3) model in the presence of deformation dependent mass formalism, investigation the X(3) model in the non-commutative space, is the other content that was studied in this thesis.