The fast blood stream of animals is associated with large shear stresses. Consequently, blood cells have evolved a special morphology and a specific internal architecture allowing them to maintain their integrity over several weeks. For instance, non-mammalian red blood cells, mammalian erythroblasts and platelets have a peripheral ring of microtubules, called the marginal band, that flattens the overall cell morphology by pushing on the cell cortex. In this article, we model how the shape of these cells stems from the balance between marginal band elasticity and cortical tension. We predict that the diameter of the cell scales with the total microtubule polymer, and verify the predicted law across a wide range of species. Our analysis also shows that the combination of the marginal band rigidity and cortical tension increases the ability of the cell to withstand forces without deformation. Finally, we model the marginal band coiling that occurs during the disc-to-sphere transition observed for instance at the onset of blood platelet activation. We show that when cortical tension increases faster than crosslinkers can unbind, the marginal band will coil, whereas if the tension increases slower, the marginal band may shorten as microtubules slide relative to each other. . This is not however the case for blood cells as they circulate freely within the fluid environment of the blood plasma. Red blood cells (RBC) and thrombocytes in non-mammalian animals [2,3], platelets and erythroblasts in mammals [4, 5] adopt a simple ellipsoidal shape (Fig. 1A). This shape is determined by two components: a ring of MTs, called the marginal band (MB), and a protein cortex at the cell periphery.In the case of platelets and non-mammalian red blood cells, both components are relatively well characterized (Fig. 1). The cortex is a composite structure made of spectrin, actin and intermediate filaments (Fig. 1B), and its complex architecture is likely to be dynamic [11][12][13]. It is a thin network under tension [14], that on its own would lead to a spherical morphology [15]. This effect is counterbalanced by the MB, a ring made of multiple dynamic MTs, held together by crosslinkers and molecular motors into a closed circular bundle [4, 16] (Fig. 1C). The MB is essential to maintain the flat morphology, and treatment with a MT destabilising agent causes platelets to round up [17]. It was also reported that when the cell is activated, the MB is often seen to buckle [3]. This phenomenon is reminiscent of the buckling of a closed elastic ring [18], but the MB is not a continuous structure of constant length.Indeed, an important feature of the MB is that is it made of multiple MTs, connected by dynamic crosslinkers. The rearrangement of connectors could allow MTs to slide relative to one another, and thus would allow the length of the MB to change. Secondly, MT growth or depolymerisation would also induce reorganisation. However, in the absence of sliding, elongation or shortening of single MTs would principally affect the thickness ...