The difficulty of eradicating memory of powder-particle interfaces in UHMWPE for bearing surfaces for hip and knee replacements is well-known, and 'fusion defects' have been implicated frequently in joint failures. During processing the polymer is formed into solid directly from the reactor powder, under pressure and at temperatures above the melting point, and two types of inter-particle defect occur: Type 1 (consolidation-deficient) and Type 2 (diffusion-deficient). To gain quantitative information on the extent of the problem, the formation of macroscopic butt welds in this material was studied, by (1) modelling the process and (2) measuring experimentally the resultant evolution of interface toughness. This paper reports on the model. A quantitative measure of interface structural integrity is defined, and related to the "maximum reptated molecular weight" introduced previously. The model assumes an idealised surface topography. It is used to calculate the evolution of interface integrity during welding, for given values of temperature, pressure, and parameters describing the surfaces, and a given molar mass distribution. Only four material properties are needed for the calculation; all of them available for polyethylene. The model shows that, for UHMWPE typically employed in knee transplants, the rate of eradication of Type 1 defects is highly sensitive to surface topography, process temperature and pressure. Also, even if Type 1 defects are prevented, Type 2 defects heal extremely slowly. They must be an intrinsic feature of UHMWPE for all reasonable forming conditions, and products and forming processes should be designed accordingly.