This thesis explores one kind of equation used to model the physics behind one beam with two ends fixed. Initially, Woinowsky Krieger sets a nonlinear partial differential equation (PDE) model by attaching one nonlinear term to the classic linear beam equation. From Zdzislaw Brezezniak, Bohdan Maslowski, Jan Seidler, they demonstrate this model mixed with one Brownian motion term describing random fluctuation. After stochastic modifications, this model becomes more accurate to the behaviors of beam vibrations in reality, and theoretically, the solution has better properties. In this thesis, the model includes more complex noises which cover the condition of random uncontinuous disturbance in the language of Poisson random measure. The major breakthrough of this work is the proof of existence and uniqueness of solutions to this stochastic beam equation and solves the flaws of previous work on proof.