This is the peer reviewed version of the following article: Pavlicek, S., Xia, J. and Mang, H. A. (2014), Numerical Solution of the Consistently Linearized Eigenproblem by Means of a Finite Difference Expression for Approximation of a Directional Derivative in MSC.MARC. Proc. Appl. Math. Mech., 14: 199200, which has been published in final form at http://dx.doi.org/10.1002/pamm.201410087. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.