Helium formation is studied in a class of exact radiation-filled cosmological models in which the space-time geometry is represented by the Friedmann-Robertson-Walker metric and the source of the gravitational field is a non-co-moving imperfect fluid. Using the methods described by Barrow (1984) we find it possible to calculate the predicted helium-4 abundance in the class of radiative models analytically in terms of the results in the corresponding standard model. It is found that different amounts of helium-4 are produced at different space-time locations in the models. It is also found that while there is less helium-4 produced than in the standard model, the models give rise to predictions for the primordial helium-4 abundance within the observed range. In view of current estimates for the pre-galactic helium abundance and the predictions obtained from the standard model, models in which less helium is produced are of particular interest. The techniques employed in the calculation are discussed, and the assumptions and approximations that have been made are described in some detail.