Abstract In this paper, we first supplement two groups of simplified general solution based on previous work. Those results are in terms of harmonic functions and fit for the cases of multiple eigenvalues. Then by trial and error, we obtain the fundamental solutions for three cases for a piezoelectric infinite media by giving the expressions of harmonic functions. Finally, by use of those solutions, we implement a boundary element method program to perform numerical calculations. The numerical results agree well with the analytical ones.