The purpose of the present study is to develop a procedure to carry out dynamic calculations when a flexible structure moves along an arbitrary orbit or track. Finite elements' equations of motion regarding a moving flexible structure have been derived considering a geometric nonlinearity. A finite rotational matrix was used to transfer a vector or a matrix to one regarding another reference frame. Computer programs which give an eigenvalue analysis and a time history response have been developed using the derived equations. Natural frequencies and modes of vibration for some analysis models were calculated by the eigenvalue analysis progralm. We also calculated time history responses for a large deformation in the case in which the analysis models moved along a track.