Abstract: In order to solve the boundary value problem with chaos or complicated boundary dates, such as singularity etc., it is necessary to establish the model of stochastic partial differential equation for the gravity field. This paper first constructs the conception of stochastic Sobolev spaces H₂²(Ω), then gives the stochastic Poisson integral as a generalized stochastic functional, and compares the relationships between stochastic model and determined model of Poisson integral, and indicates that determined model is just one of the special situations of stochastic Poisson integral.