Oxygen diffusion problem examines the injection of oxygen into a sick cell and diffusion of the injected oxygen inside the cell. Mathematical model of the problem has two steps. At the first step, the stable case having no oxygen transition in the isolated cell is searched while at the second step the moving boundary problem of oxygen absorbed by the tissues in the cell is searched. In this study, trace of moving boundary of the oxygen diffusion problem is determined using constrained integral method, the profile of moving boundary is determined by the third and the fourth order polynoms, and the results are compared with the preceding studies. (C) 2002 Elsevier Inc. All rights reserved.