In the annual June Enumerative Surveys (JES) of the U.S. Department of Agriculture (USDA), the area frame sampling involves multiyear rotation designs with 20% replacement of sample units each year. Currently, USDA uses the latest year sample data almost exclusively in its estimation procedure. We propose that the multiyear sample survey data should be used for estimation of crop acreages and livestock. We develop a multiyear estimation method based on an analysis of variance model that takes into account the successive sampling of units in the area frame from year to year. The proposed method is applied to estimate the 1989 hogs and soybean acreages using JES data for three years: 1987, 1988, and 1989. These estimates are compared with those obtained using the current USDA estimation method. We give relative efficiencies of the multiyear estimates compared to the single-year estimates, often showing a substantial improvement in precision. We also make an evaluation study of the proposed estimation method using simulations and show it to be fairly robust to misspecification of the model parameter.