Reserve (or field) growth, which is an appreciation of total ultimate reserves through time, is a well-recognized phenomenon, particularly in mature petroleum provinces. 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. During a five-year (1992-1996), the original Arrington method gave 1.03% higher than the actual oil reserve growth, whereas the proposed modified method gave a value within 0.3% of the actual growth, and therefore it was accepted for the development for reserve growth models. During a five-year (1992-1996), the USGS 1995 National Assessment gave 39.3% higher oil and 33.6% lower gas than the actual growths, whereas the new model based on Modified Arrington method gave 11.9% higher oil and 29.8% lower gas than the actual growths. The new models forecast predict reserve growths of 4.2 billion barrels of oil (2.7%) and 30.2 trillion cubic feet of gas (5.4%) for the conterminous U.S. for the next five years (1997-2001). ?? 2005 International Association for Mathematical Geology.