Modified atmosphere packing (MAP) is a technique to increase the shelf life of fresh meat. Continuing development of MAP requires better understanding of the physical and chemical processes taking place, in particular the diffusion of oxygen and its reaction with myoglobin. We model these processes using reaction-diffusion equations. The reactions include binding of oxygen to myoglobin, oxidation of myoglobin and other oxygen consuming processes. Model parameters have been extrapolated using data from the literature to relevant temperatures and pH values. Partial agreement with spatially resolved pigment concentration data is obtained, but only by substantially increasing the value of the oxygen consumption rate. Application of the model to meat stored at 5 °C shows that the metmyoglobin layer forms under the surface over a time scale of 24 h; The metmyoglobin layer forms deeper inside the meat proportional to the logarithm of the headspace oxygen partial pressure, thus improving the colour appearance of the meat.