<p>The nonlinear vibration analysis of structural elements such as beams has been a pretty appealing topic among scientists. The nonlinear vibration behavior of a non-uniform beam with stepwise variations in geometry, resting on an elastic foundation and subjected to a magnetic field, is theoretically investigated in the present manuscript. The governing equations are established by dint of Hamilton’s principle. A parametric study is conducted considering the variational parameters of the non-uniform beam, including various boundary conditions, the geometric cross-sectional ratio, and the step location. In the numerical results, the linear natural frequencies are presented in tables. The nonlinear frequency to linear frequency ratio curves are shown in the figures. In addition, the article was completed by investigating the case of internal resonance. The theoretical results are also compared with previous scientific works to prove the accuracy of the applied methods and they show good consistency. The results indicate that the natural frequencies exhibit strong sensitivity to the sectional ratio, step location, and boundary conditions. It is observed that natural frequencies rise with increasing magnetic field and elastic foundation effects. Furthermore, the change of the nonlinear to linear natural frequency ratio graphs with varying magnetic force, linear and nonlinear foundation coefficients have indicated the significant effects of those variable parameters in beams.</p>