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A generalized oscillator model for nonlinear vibration analysis of various mechanical systems was proposed and solved using the quasi-static cubication method. The proposed generalized oscillator model is useful for introducing and discussing the nonlinear vibration models of several oscillatory systems. To establish the accuracy of the quasi-static cubication method for the generalized oscillator model, a number of simulations were carried out for the nonlinear vibration models of common mechanical systems derived from the generalized oscillator model. The results obtained were found to be in good agreement with exact solutions and other approximate solutions found in the literature. Furthermore, the quasi-static cubication method was found to be accurate for a wide range of oscillation amplitudes. A significant feature of the quasi-static cubication method is its simplicity and accuracy; hence, it is considered an efficient technique for nonlinear vibration analysis in undergraduate and post-graduate courses on dynamics. [ABSTRACT FROM AUTHOR]