Summary: A unified theory for the general solutions of three-dimensional elasticity is employed to transform the governing equations of plane piezoelectricity into three generalized Laplace equations. The latter equations are uncoupled and can be pursued separately. By introducing three generalized complex variables, the complete solution sets for plane piezoelectricity are constructed. By adopting the constituents in the solution sets as the trial functions, the Trefftz collocation and the Trefftz Galerkin methods are formulated. Both methods fall into the category of Trefftz indirect methods as the coefficients of their trial functions are non-physical. Numerical examples are presented to illustrate the efficacy of the formulations.