It is well known that mesh densities quantitatively influence FEA predictions. A coarse mesh may lead to inaccurate predictions while a finer mesh tends to produce more accurate predictions. In engineering practice, especially for the analysis of a multibody assembly, it is not practical to have very fine mesh in the FEA model. There are various mesh guidelines to have a reasonably sized mesh that produces accurate predictions in contact problems, e.g., a finer mesh for the slave surface. An evaluation of a 4-body assembly with substantial differences in the hardness and yield strengths led to the revelation that relative mesh sizes influence the deformation of the components in the assembly qualitatively, potentially leading to erroneous trends. It is determined that the meshes at the contact surfaces should be about the same size to correctly differentiate the differences in yield strengths of the components. The finding is verified by a model with a very fine mesh for all components. This finding, i.e., similar sized relative fine meshes at contact surfaces, is used as a guideline for the analysis of an expandable liner hanger deployed in casings with various yield strengths. The numerical predictions are consistent with mechanistic considerations, and correlate with test observations. It is recommended to use the proposed mesh guideline for improvement of multibody contact analysis quality.