This study focused on the vibration behavior of a modified vertical conveyor system. The calculated system is exhibited by 2-degree-of-freedom counting quadratic and cubic nonlinearities among both external and parametric forces. Technique of multiple scales connected to gain approximate solutions and study stability of measured structure. All resonances from mathematical solution are extracted. The performance of the system is measured by means of Runge–Kutta fourth-order process (e.g., ode45 in MATLAB). Moreover, two simultaneous resonance cases of this system have been studied analytically and numerically. Stability of acquired numerical solution discovered via frequency response equations. Influences contained by important coefficients scheduled frequency response curves of the considered structure are studied inside numerical results. Methodical results obtained in this work agreed well through the numerical outcome. The description outcome is matched up to available recently published articles.