The influence of decaying longitudinal pulses excited by a vehicle bumping at bridge abutment and expansion joints on the behavior of prestressed box beams was investigated.The analysis on the excessive vibration of the beam induced by longitudinal pulses and traffic load was carried out by using dynamic stability theory.Via functional transformation of the equilibrium equation,the method of subdomain weighted residuals was used to solve the corresponding homogeneous differential equation of vibration on the beam with non-uniform cross-section.Different solution groups were obtained by using different trial functions.The eigenvalues that indicated divergent property of the equation solutions were obtained depending on the relative velocity and acceleration defined in this paper.The instable regions of the beams oscillation were determined via approximate treatment and numerical verification of the treatment was carried out.The influence of the damp and pre-applied force on instable region of the beam subjected to longitudinal pulses and traffic load was discussed and it was different from influence on condition that single periodic load was applied to the beam.Overvibration analysis of the beam based on the eigenvalues of increasing acceleration was developed.The further use of the eigenvalues was demonstrated.The analysis on overvibration of Bridge Crossing X Depot was also demonstrated as an example in appraisal of excessive vibration of highway bridges.The analysis and computation were implemented via subroutines which were programmed using Maple mathematical software package.