Methods are presented for estimating the magnitude and frequency of peak discharges of streams in Arkansas. Regression analyses were developed in which a stream's physical and flood characteristics were related. Four sets of regional regression equations were derived to predict peak discharges with selected recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years on streams draining less than 7,770 square kilometers. The regression analyses indicate that size of drainage area, main channel slope, mean basin elevation, and the basin shape factor were the most significant basin characteristics that affect magnitude and frequency of floods. The region of influence method is included in this report. This method is still being improved and is to be considered only as a second alternative to the standard method of producing regional regression equations. This method estimates unique regression equations for each recurrence interval for each ungaged site. The regression analyses indicate that size of drainage area, main channel slope, mean annual precipitation, mean basin elevation, and the basin shape factor were the most significant basin and climatic characteristics that affect magnitude and frequency of floods for this method. Certain recommendations on the use of this method are provided. A method is described for estimating the magnitude and frequency of peak discharges of streams for urban areas in Arkansas. The method is from a nationwide U.S. Geeological Survey flood frequency report which uses urban basin characteristics combined with rural discharges to estimate urban discharges. Annual peak discharges from 204 gaging stations, with drainage areas less than 7,770 square kilometers and at least 10 years of unregulated record, were used in the analysis. These data provide the basis for this analysis and are published in the Appendix of this report as supplemental data. Large rivers such as the Red, Arkansas, White, Black, St. Francis, Mississippi, and Ouachita Rivers have floodflow characteristics that differ from those of smaller tributary streams and were treated individually. Regional regression equations are not applicable to these large rivers. The magnitude and frequency of floods along these rivers are based on specific station data. This section is provided in the Appendix and has not been updated since the last Arkansas flood frequency report (1987b), but is included at the request of the cooperator.