defined as the ratio of the viscous force relative to the elastic force due to membrane deformation. It is worth mentioning that, larger Ca leads to a larger RBC deformation and a larger orbit for the inter-face point to circulate. Our simulations are performed at Re = 0.1 and Ca = 0.5 (for tank-treading) and Ca = 0.1 (for tumbling motion). The values of other constant parameters associated respectively with the fluid domain and the viscoelastic immersed boundary, are tabulated in Tables 1 and 2. It should be noted that the values of cs and cb given in Table 2 are identical to those considered in the work by Franke et al. [25].