Reserve (or field) growth is an appreciation of total ultimate reserves through time and is observed throughout the productive lives of oil and gas fields in all petroleum provinces? but most especially in mature petroleum provinces (like many in the United States) when the rate of finding new discoveries reduces to a low level. The importance of forecasting reserve growth accurately in a mature petroleum province made it necessary to develop improved growth functions, and a critical review of the original Arrington method was undertaken. A modification of the pioneering Arrington (1960) method for estimating reserve growth suggests that, as a basis for optimum reserve growth functions, cumulative growth factor smoothing produces a better match with known volume data than does annual growth factor smoothing. Cumulative growth factor smoothing is thus the basis for the building of reserve growth functions in this study. Estimates of oil and gas growth during 1992?1996 based on the modified Arrington method are closer to the actual volumes than those based on the functions from 1995 National Assessment. The new growth functions predict an average annual reserve growth of 0.42 percent per year for oil and 0.90 percent per year for gas over a 30-year (1996?2026) period.