Stationary probability density function (PDF) solution of responses of nonlinear stochastic systems subjected to Poisson white noise is analyzed. The PDF solutions are obtained with exponential polynomial closure (EPC) method. In order to evaluate the effectiveness of this method, two oscillators are investigated. One is about a stochastic nonlinear system excited by additive Poisson excitation. Both nonlinear damping force and nonlinear stiffness force are considered in this example. Another is about a Duffing oscillator excited by both additive and multiplicative Poisson white noises. Compared with the results from Monte Carlo simulation, good agreement is achieved in both examples, especially in the tail region of PDFs of system responses