Force-extension data, obtained at 140°C on polyethylene monofilaments, electron-irradiated with doses from 0.7 to 6.0 Mrad, are interpreted according to a recent model of rubber elasticity proposed by Edwards and Vilgis. In this model, the free energy of single chains between the crosslinks, N c, is described by the usual statistical theory, whereas the reduction of entropy due to entanglements with neighbouring chains is described by a number, N s, of slip links, which are free to slide along the arc length of the chain between crosslinks. The degree of slip link freedom is measured by a parameter η. Finally, the extra constraints introduced by the entanglements limit the extensibility of the chains long before the single chain limit is reached. In the Edwards' model this introduces a further parameter α. Using these four parameters ( N c, N s, η, α), good fits are obtained to all sets of data. The parameter α is shown to describe particularly well the increase in the reduced stress at high deformation, observed for the more highly crosslinked samples. Both N c and N s increase monotonically with dose, indicating that each crosslink renders effective a certain number of topological entanglements. The parameter η is essentially constant at about 1.1, a higher value than that found by other workers. The theoretical value of 0.2343 is shown to be not applicable for these samples. The effect of strain rate and orientation history on the samples is also described. Our data suggest that slip links are dynamic, and can behave as crosslinks, at higher strain rate. The effect of solid state drawing on an irradiated polymer is to alter permanently the structure of the network; increasing the number of effective crosslinks, at higher dose, and removing a fraction of non-permanent entanglements, at lower dose.