The magnitude and frequency of peak discharges on streams in Arkansas, were estimated through the use of comprehensive regression analyses, in which physical characteristics of streams were related to flood characteristics at gaging stations. Equations derived from the regression analyses provide estimates of peak discharges with selected recurrence intervals from 2 to 100 yrs on streams that have drainage areas < 3,000 sq mi. The regression analyses indicate that size of drainage area, slope of the main channel, length of the main channel, elevation of the basin, and mean annual precipitation were the most significant basin and climatic characteristics that affect the magnitude and frequency of floods. A technique is presented for estimating a stage-discharge relation at ungaged sites based on a cross section determined from topographic maps. This cross-section and stage-discharge relation is then used to determine the hydraulic radius for the discharges at each recurrence interval. Techniques are presented for estimating the magnitude and frequency of peak discharges using the hydraulic radius with other physical characteristics of the basin. The techniques that use the hydraulic radius give standard errors of estimate from 5% to 16% lower than techniques that do not use hydraulic radius. Data from 200 gaging stations with drainage areas less than 3,000 sq mi and with at least 10 yrs of record were used in the analyses. Large rivers such as the Red, Arkansas, White, Black, St. Francis, Mississippi, and Ouachita Rivers have flood flow characteristics that differ from those of smaller tributary streams and were, therefore, treated individually. Regional regression equations are not applicable to the large rivers; the magnitude and frequency of floods along these rivers are based on station data. A method is described for estimating the magnitude and frequency of peak discharges on streams for urban areas in Arkansas. (Lantz-PTT)