In this paper,the three-dimensional inverse Cauchy problems for the Laplace equation in a multiply connected domain using the collocation Trefftz method and the method of fundamental solutions were investigated.We first introduced the solutions of three dimensional inverse Cauchy problems using the collocation Trefftz method based on cylindrical harmonics.The numerical solutions were then approximated by superpositioning T-complete functions formulated from 36 independent functions satisfying the governing equation in the cylindrical coordinate system.To deal with complicated problems in a multiply connected domain,we adopted the generalized multiple source point boundary collocation Trefftz method which allows many source points in the Trefftz formulation without using the decomposition of the problem domain.In addition to the collocation Trefftz method,we adopted the method of fundamental solutions to solve three dimensional inverse Cauchy problems.Comparisons of the collocation Trefftz method and the method of fundamental solutions for solving three-dimensional inverse Cauchy problems for the Laplace equation were made.The results revealed that the collocation Trefftz method demonstrates much better capability than the method of fundamental solutions for solving the three-dimensional inverse Cauchy problems and can recover the unknown data with high accuracy,even though the over specified data were provided only at a 1/6 portion of the overall boundary.