Flexible displays have been evolved into curved, foldable, and rollable as the degree of bending increases. Due to the presence of brittle electrodes (e.g. indium-tin oxide (ITO)) that easily cracked and delaminated under severe bending deformation, lowering mechanical stress of the electrodes has been critical issue. Because of this, mechanical stress of brittle electrode in flexible displays has been analyzed mostly in terms of bending radius. On the other hand, in order to make rollable display, various mechanical components such as roller and spring are needed to roll-up or extend the screen for the rollable display apparatus. By these mechanical components, brittle electrode in the rollable display is subjected to the excessive tensile stress due to the retracting force as well as the bending stress by the roller. In this study, mechanical deformation of rollable OLED display was modeled considering boundary conditions of the apparatus. An analytical modeling based on the classical beam theory was introduced in order to investigate the mechanical behavior of the rollable display. In addition, finite element analysis (FEA) was used to analyze the effect of mechanical components in the apparatus on the brittle electrode. Furthermore, a strategy for improving the mechanical reliability of the rollable display was suggested through controlling the stiffness of adhesives in the display panel.