Two precise transfer matrix formulae of different forms for analysis of shaft element with constant section parameters are derived which take axial forces and shearing deformation into account.Both of the formulae are applied to a practical example.The comparison between the results of the calculation and experimental data shows that the precision of the formulae is very well and that considerable axial forces do have a nonnegligible influence on dynamic properties of rotor bases system.The presented formulae not only extend the application of the transfer matrix method

but also provide a convenient approach to solving the specific engineering problems in dynamic analysis of the rotor bases system with considerable axial forces due to pre pressed coupling curves in its assemblage.