Living cells are modified at their surface with specially selected polymers. Covalently attaching specially selected polyethylene glycol (PEG) derivatives to the surface of red blood cells (RBC) in aqueous media under mild conditions is a preferred example. The selected PEG derivatives dramatically reduced aggregation and low shear viscosity of RBC resuspended in autologous plasma, and inhibited RBC agglutination by blood group-specific antibodies. The morphology and deformability of the PEG-treated cells were unaltered. PEG coating of the RBC surface is applicable to the treatment of a variety of diseases characterized by vaso-occlusion or impaired blood flow, e.g., myocardial infarction, shock, and sickle cell disease. An infusion solution is prepared containing red blood cells covalently bound to a PEG derivative having a molecular weight of between 2,000 and 5,000 Daltons and a PEG derivative having a molecular weight between 10,000 and 35,000 Daltons.