The nuclear two – parameters softness model has been used to calculate the energy levels of the ground state bands in even - even actinide nuclei namely228,230Th, 230-238 U,236-244Pu, 242-248 Cm, 248,250Fm and 252,254 No. For each band the optimum values of the softness parameter and the ground state moment of inertia are calculated by the fitting procedure between the calculated and the experimental excitation energies using a computer simulated search program. Very good agreement is found between the calculated and experimental data. The nuclear kinematic and dynamic moments of inertia have been calculated; a smooth gradual increase in both moments of inertia as function of rotational frequency was seen. The Δ I = 2 energy staggering index represents the finite difference approximation of fourth order derivative of the transition energies is extracted and examined. The transition energies in the ground state bands of 236U and 238U have quite identical energies within 2 KeV up to spin 24 ħ, which indicate that the phenomenon of identical bands is not restricted to superdeformed bands. The study indicates also that these conjugate pair of nuclei 236U and 238Uhave moments of inertia nearly identical. The potential energy surfaces for isotones 234Th,236Uand 238Pu are calculated and show rotational behavior mainly prolate deformed.