In　biaxial　contouring　control　applications,　the　inherent　structural　flexibility　of　machines　can　lead　to　position　discrepancies　between　the　manipulator　and　actuator,　and　thus　deteriorate　the　manufacturing　performance,　especially　when　the　controller　is　designed　without　available　end-effector　side　feedback.　In　this　work,　we　focus　on　the　end-effector　contouring　control　problem　for　industrial　machines　with　position-dependent　flexibility　to　improve　the　contouring　performance　while　eliminating　the　effect　of　mechanical　vibration.　A　model　for　the　widely　used　cantilever　beam　machine　is　developed　to　describe　the　dynamics　of　the　end-effector　by　capturing　the　rotation　and　coupled　dynamics　between　axes.　The　proposed　model　is　validated　through　experiment　and　systematically　reduced　to　switched　linear　time-invariant　models　for　controller　design.　By　adopting　the　extended　state　observer,　the　proposed　control　architecture　decouples　the　dynamics　between　the　X　and　Y-axis　and　simplifies　the　controller　design　process.　The　model　predictive　control　method　is　utilised　for　improving　the　contouring　performance　while　reducing　mechanical　vibration.　The　efficacy　of　the　proposed　control　framework　is　demonstrated　and　validated　on　the　designed　high-fidelity　model.　Performance　comparisons　between　the　proposed　approach　with　benchmark　controllers　are　presented.