Purpose <p>The Duffing equation has been widely used as the test example of methods and techniques for nonlinear problems in vibrations. With its wide appearances in many vibration problems, solutions including the exact form in the elliptic functions and various approximation based on the asymptotic approaches have been presented. These solutions are widely used as the demonstration of advantages and efficiency of methods and techniques needed in meeting the ubiquitous demands in solving the nonlinear differential equations of vibrations.</p> Methods <p>A generalized Duffing equation with the restoring force as a tangential function is solved with the extended Galerkin method in this study by expanding the tangential function in power series of different orders, and the accuracy is checked with the numerical results from the exact solutions.</p> Results and Conclusions <p>The results shown that the increase of terms of power series expansion and higher-order harmonics will improve the accuracy of solutions, and the combination of approximations of trigonometric functions with the extended Galerkin method and procedure are capable and effective in solving the generalized Duffing equations for approximate solutions.</p>