A　new　and　efficient　computation　of　normal　forms　is　developed　in　this　paper　for　high　dimensional　nonlinear　systems,　and　the　computational　method　is　applied　to　nonplanar　motion　of　a　cantilever　beam.　The　method　is　based　on　the　adjoint　operator　method　and　has　the　advantage　of　directly　calculating　coefficients　of　normal　forms.　Moreover,　the　new　method　is　easy　to　apply　to　engineering　applications,　and　the　final　partial　differential　equations　of　various　resonant　cases　appear　in　a　canonical　form　whose　solutions　can　be　conveniently　obtained　using　polynomial　equations.　With　the　aid　of　the　Maple　software,　a　symbolic　program　for　computing　the　normal　forms　of　high　dimensional　nonlinear　systems　is　developed.　Based　on　the　symbolic　program,　the　normal　forms　and　their　coefficients　of　the　averaged　equations　for　nonplanar　motions　of　a　cantilever　beam　are　calculated　for　two　resonant　cases.