This paper is concerned with two issues that arise in the finite element analysis of 3D solids. The first issue examines the objectivity of various stress rates that are adopted in incremental analysis of solids. In doing so, it is revealed that large errors are incurred by an improper choice of stress rate. An example problem is presented to show the implications of the choice of stress rate. The second issue addresses the need to maintain work-conjugacy in formulating and solving bifurcation buckling problems of 3D elastic solids. Four popular commercial codes are used to obtain buckling loads of an axially compressed thick sandwich panel, and it is shown that large errors in buckling load predictions are incurred as a result of violating the requirement of work-conjugacy. Remedies to fix the errors in the numerical solution strategy are given.