The Poisson equation can be solved by first finding a particular solution and then solving the resulting Laplace equation. In this paper, a computational procedure based on the Trefftz method is developed to solve the Poisson equation for two-dimensional domains. The radial basis function approach is used to find an approximate particular solution for the Poisson equation. Then, two kinds of Trefftz methods, the T-Trefftz method and F-Trefftz method, are adopted to solve the resulting Laplace equation. In order to deal with the possible ill-posed behaviors existing in the Trefftz methods, the truncated singular value decomposition method and L-curve concept are both employed. The Poisson equation of the type, ∇ 2 u = f(x, u), in which x is the position and u is the dependent variable, is solved by the iterative procedure. Numerical examples are provided to show the validity of the proposed numerical methods and some interesting phenomena are carefully discussed while solving the Helmholtz equation as a Poisson equation. It is concluded that the F-Trefftz method can deal with a multiply connected domain with genus p(p > 1) while the T-Trefftz method can only deal with a multiply connected domain with genus 1 if the domain partition technique is not adopted.