The present study aims to use a combined LBIBM method to investigate the twodimensional (2D) motion and deformation of mass less RBCs in the capillary. The distinct feature of the method used here is to employ the combination of simple Peskin’s IBM and standard LBM to capture essential flow physics like that of the RBC in the tank-treading motion. It may be noted that the arrangement of Lagrangian points on the immersed boundary plays a major role in the accuracy of the simulation results: for higher deformations, higher resolutions are required. Therefore, in order to obtain more accurate and truthful solutions, a higher density of Lagrangian points was used on those parts of the immersed boundary located close to the channel’s bottom wall, where they experience greater deformation due to the greater shear forces. This nonuniform distribution of Lagrangian points along with a modified Dirac delta function was found to give more realistic results than those methods, which use uniform distribution of Lagrangian points and Peskin’s original delta function (it is noteworthy that,extension of this method to three dimensional problems can be done in a straightforward way (see also [23])). In addition, in this work, the behavior of healthy and sick RBCs, which differ by their stiffness, when moving in the capillary is studied and can be clearly discerned.