Purpose <p>In this paper, we have studied the natural vibration and steady-state forced vibration of the rectangular plate with welding residual stress by the analytical method.</p> Method <p>Based on the residual stress distribution near the weld seam of the welded plate, the residual stress distribution is assumed as a polynomial shape.&#xa0;Next, the natural vibration equations for the plate with residual stress are solved analytically using the Hamiltonian principle to determine the natural frequencies and modes of vibration.&#xa0;In addition, the solution of steady-state forced vibration is found for the welded plate regarding residual stress under the concentrated harmonic loading, the dynamic stress is determined, and a method is proposed to determine the frequencies and the magnitude of excitation force required for vibration stress relief.</p> Result <p>The first to fourth natural frequencies of rectangular plate with residual stress are increased by 19.6%, 15.1%, 29.0% and 13.6% compared to the case without residual stress, respectively. Also, the vibration amplitude of rectangular plate due to lumped harmonic load with a frequency close to the first natural frequency is much larger, 10 times, than that of the case with frequencies close to the other natural frequencies. As the amplitude of dynamic load gets increased and the more the frequency approaches the natural frequency, the greater the total equivalent stress that occurs in the plate gets.</p> Conclusion <p>We have proposed a method to evaluate the vibration characteristics of rectangular plates with residual stresses and to determine the frequency and magnitude of the excitation force required for vibration stress relief. The proposed method can be extended to determine the vibration characteristics and vibration stress relief parameters of rectangular plates with arbitrary residual stress distribution.</p>