¨ The Mobius strip, a mathematical construction from geometry, is formed by twisting one end of a flat strip by 180 degrees with respect to the other before attaching the ends to form a closed loop. Finding the actual equilibrium shape of ¨ such an elastic Mobius strip is a significant challenge in computational mechanics. Recent efforts in the 80 year history of this problem lie between the boundaries of traditional mechanics and geometry, sometimes producing conflicting approaches and results. This work explores the source of the discrepancies by employing three different models. Equilibrium configurations are calculated for a standard Kirchhoff rod model, for a more general Cosserat rod model, and for a developable surface model due to Wunderlich. More importantly, this is the ¨ first study that analyzes the mechanical stability of elastic Mobius strip equilibria.