Journal sliding bearings are often used to support rotating machinery to add damping and increase load capacity. These bearings have strong nonlinearities that can cause vibration problems. Various studies have been conducted on vibration phenomena caused by nonlinearities in journal sliding bearings. However, most of these studies have been on horizontally supported rotating machines. Some of these techniques are difficult to apply to vertically supported rotating machines. The most significant difference between horizontal and vertical support is that the weight of the rotor does not act on the journal sliding bearing in the case of vertical support. Therefore, it is not appropriate to use the horizontal journal sliding bearing theory based on the equilibrium point for the vertical shaft rather it should be considered based on the whirling orbit. In this paper, the nonlinear rotor dynamics of vertical rotating machines with journal sliding bearings are investigated and evaluated by theoretical and numerical analyses and experiments of a simple vertical rotating shaft. As a result, some new destabilization and stabilization phenomena are found in the vertical shaft system, and it is clarified that they cannot be predicted by the conventional linear analysis around the equilibrium point but can be predicted by the nonlinear dynamical analysis of the whirling orbit. Particularly, these destabilization and stabilization phenomena of the vertical shaft system are strongly affected by the magnitude of the vibration in the journal sliding bearing due to its nonlinearity, and the unbalance of the rotating body can be a parameter to control them.