The theory of void swelling in irradiated steels has been critically re-examined and a model has been developed from first principles for such fundamental parameters as the bias factors for dislocations and voids, relaxation volumes for interstitials and vacancies, and migration and formation energies for interstitials and vacancies. Four types of growth mechanisms are modeled: self-interstitial emission, loop punching, thermal vacancy exchange, and bias driven growth. The net bias of the system is allowed to change continuously with the evolving microstructure. Combining these growth mechanisms has resulted in a swelling model capable of reproducing some important features of the observed swelling behavior in austenitic stainless steels. For austenitic stainless steels, the model predicts bias driven growth for temperatures between 300°C and 600°C. The long-term swelling rate in this temperature range is roughly independent of temperature and helium concentration and is between 0.7%/dpa (displacements per atom) and 1.3%/dpa. For ferrite phase, the model predicts bias driven growth for temperatures between 300°C and 500°C. However, for this class of steel, the swelling rate is at or below 0.3%/dpa. For bias driven growth, it has been shown that the interstitial and vacancy relaxation volumes ultimately determine the maximum possible swelling rate. It is for this reason that the model predicts a much lower swelling rate for ferrite phase than for austenitic stainless steels.