With Gallerkin’s method, the stretched Euler-Bernoulli beam with its two ends pin-supported is described as multi-degreeof-freedomsystem. TheprobabilisticsolutionoftheMDOFnonlinearstochasticsystemsexcitedbyPoissonwhitenoiseisinvestigated with the state-space-split method and exponential-polynomial closure method proposed by the author. Numerical results show that the results obtained with the state-space-split method and exponential-polynomial closure method agree well with the simulation for the stretched Euler-Bernoulli beam excited by uniformly distributed Poisson white noise.