Described herein is a technique for covalently modifying tissue and cellular surfaces to inhibit cell adhesion. The process described herein is conducted under conditions tolerable in vivo and employs a biocompatible polymer having a reactive group attached to at least one end that reacts with groups present or on tissue and cellular surfaces under aqueous and mild conditions and thereby covalently attaches the polymer to the tissue or cellular surface. Preferably, the reactive group attached to the polymer reacts with amines and hydroxyls present on tissue and cellular surfaces. In one preferred embodiment, the methods described herein provide for the covalent modification of tissue and cellular surfaces using a PEG-diisocyanate solution. The methods described herein are particularly useful in impairing platelet and leukocyte deposition in blood vessels and thereby thwarting thrombosis and restenosis, a common complication of vascular procedures including PTCA and vascular surgery. Furthermore, by masking the tissue surface proteins from blood elements, the methods described herein are useful in decreasing graft thrombogenicity and reducing the complications of vascular surgery. Finally the methods described herein reduce the immunogenicity of transplanted tissues and cells and thereby reduce the need for immunosuppressive therapy.