Abstract: The so-called Poisson gravimetry boundary value problems, i. e. Stokes problem and Neumann problem for Poisson equation with respect to the disturbing potential, are formaulated in this paper. For solving these two kinds of problems, firstly, Dirichlet problem for Poisson equation is investigated and its integral solution is written out with respect to second Green identity; secondly, by introducing two auxilary functions. respectively. Stokes and Neumann problems for Poisson equation are deduced to Dirichlet problem of sorts, so that their integral solutions are shown in an easy way. The final solutions become a anaddition of two parts. where one is responsive to boundary data, and another to topographies.The present procedure given in this paper opens a new way to study of fining the geoid by using topographies.