Borehole drillstring waves play an important role in geotechnical and exploration applications. Coupled waves are simulated inside and outside a real drillstring in borehole. The drillstring is considered a system with variable geometry. We simulated coupled waves in three domains: in-ner mud, drillstring, and annular mud. Each mode has a characteristic wave propagation velocity. A consequence of this coupling effect is that waves from the downhole tool can be partially re-flected and converted to other modes at a discontinuity in the formation stiffness or in the annular cross section that can cause a significant reduction of the transmitted wave energy. Examples of application are reported.