We　consider　the　three　dimensional　Cauchy　problem　for　the　Laplace　equation　where　the　data　is　given　at　z　=　0　and　a　solution　is　sought　in　the　region　x,y　∈　R,0　＜　z　＜　1.　The　problem　is　ill-posed,　the　solution　(if　it　exists)　doesn＇t　depend　continuously　on　the　initial　data.　Using　Galerkin　method　and　Meyer　wavelets,　we　get　the　uniform　stable　wavelet　approximate　solution.　Furthermore,　we　shall　give　a　recipe　for　choosing　the　coarse　level　resolution.　©　2011　Editorial　Board　of　Analysis　in　Theory　and　Applications　and　Springer-Verlag　Berlin　Heidelberg.