Inthispaper,anewnumericalmethodfortheSignoriniprobleminthree-dimensionalelasticityispresented.Theproblemisreducedtoaboundaryvariationalinequalitybasedonanewrepresentationofthederivativeofthedoublelayerpotential.Furthermore,aboundaryelementprocedureisdescribedforthenumericalapproximationofitssolutionandanabstracterrorestimateisgiven.