Abstract: In this paper‚a Green quas-i function is firstly set up by using the basic solution of Poissonʾs equation．This function satisfies the homogeneous boundary condition of Poissonʾs equation．Next‚the boundary value problem is changed into an integral equation by applying a Green function．Then‚by establishing a normalized boundary equation‚the irregularity of the kernel of integral equation is overcome．The elastic torsion can be considered as a boundary value problem of Poissonʾs equation．For any complicated area‚a normalized boundary equation can always be found according to the R-function theory‚so the elastic torsion problem can be transformed into a second-class Fredholm integral equation without irregularity．Numerically illustrated results show that the proposed method is of high accuracy and can be used to solve other complicated boundary value problems in mechanics and physics．

Key words: Green quasifunction, integral equation, Poisson?s equation, elastic torsion