ThefundamentalsolutionsoftheorthotropicthickplatestakingintoaccountthetransversesheardeformationarederivedbymeansofHrmander’soperatormethodandaplane-wavedecompositionoftheDiracδ-functioninthispapey.Theboundaryintegralequationsofthethickplateshavebeenformulatedwhichareadaptedtoarbitraryboundaryconditionsandplaneforms.Thenumericalcalculationofthefundamentalsolutionsisdiscussedindetail.SomenumericalexamplesareanalyzedwithBEM.