An all-atom phospholipid bilayer and triblock copolymer model was developed for molecular dynamics (MD) studies. These were performed to investigate the mechanism of interaction between membrane-stabilizing triblock copolymer P188 and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) lipid bilayers under applied lateral surface tension (gamma) to model membrane mechanical stress. Results showed that P188 insertion is driven by the hydrophobic poly(propylene oxide) (PPO) core and dependent on bilayer area per lipid. Moreover, insertion of P188 increased the bilayer's resistance to mechanical rupture, as observed by a significant increase in the absolute lateral pressure required to disrupt the bilayer. To further investigate the specific chemical features of P188 underlying membrane stabilizer function, a series of MD simulations with triblock copolymers of the same class as P188 but of varying chemical composition and sizes were performed. Results showed that triblock copolymer insertion into the lipid bilayer is dependent on overall copolymer hydrophobicity, with higher copolymer hydrophobicity requiring a reduced bilayer area per lipid ratio for insertion. Further analysis revealed that the effect of copolymer insertion on membrane mechanical integrity was also dependent on hydrophobicity. Here, P188 insertion significantly increased the absolute apparent lateral pressure required to rupture the POPC bilayer, thereby protecting the membrane against mechanical stress. In marked contrast, highly hydrophobic copolymers decreased the lateral pressure necessary for membrane rupture and thus rendering the membrane significantly more susceptible to mechanical stress. These new in silico findings align with recent experimental findings using synthetic lipid bilayers and in muscle cells in vitro and mouse models in vivo. Collectively, these data underscore the importance of PEO-PPO-PEO copolymer chemical composition in copolymer-based muscle membrane stabilization in vitro and in vivo. All-atom modeling with MD simulations holds promise for investigating novel copolymers with enhanced membrane interacting properties.