Blood banks around the world store blood components for several weeks ensuring its availability for transfusion medicine. Red blood cells (RBCs) are known to undergo compositional changes during storage, which may impact the cells' function and eventually the recipients' health. We extracted the RBC's cytoplasmic membrane (RBCcm) to study the effect of storage on the membranes' molecular structure and bending rigidity by a combination of X-ray diffraction (XRD), X-ray diffuse scattering (XDS) and coarse grained Molecular Dynamics (MD) simulations. Blood was stored in commercial blood bags for 2 and 5 weeks, respectively and compared to freshly drawn blood. Using mass spectrometry, we measured an increase of fatty acids together with a slight shift towards shorter tail lengths. We observe an increased fraction (6%) of liquid ordered (lo) domains in the RBCcms with storage time, and an increased lipid packing in these domains, leading to an increased membrane thickness and membrane order. The size of both, lo and liquid disordered (ld) lipid domains was found to decrease with increased storage time by up to 25%. XDS experiments reveal a storage dependent increase in the RBCcm's bending modulus κ by a factor of 2.8, from 1.9 kBT to 5.3 kBT. MD simulations were conducted in the absence of proteins. The results show that the membrane composition has a small contribution to the increased bending rigidity and suggests additional protein-driven mechanisms.