It is usually advantageous to use information regarding historical floods, if available, to define the flood-frequency relation for a stream. Peak stages can sometimes be determined for outstanding floods that occurred many years ago before systematic gaging of streams began. In the United States, this information is usually not available for more than 100-200 years, but in countries with long cultural histories, such as China, historical flood data are available at some sites as far back as 2,000 years or more. It is important in flood studies to be able to assign a maximum discharge rate and an associated error range to the historical flood. This paper describes the significant characteristics and uncertainties of four commonly used methods for estimating the peak discharge of a flood. These methods are: (1) rating curve (stage-discharge relation) extension; (2) slope conveyance; (3) slope area; and (4) step backwater. Logarithmic extensions of rating curves are based on theoretical plotting techniques that results in straight line extensions provided that channel shape and roughness do not change significantly. The slope-conveyance and slope-area methods are based on the Manning equation, which requires specific data on channel size, shape and roughness, as well as the water-surface slope for one or more cross-sections in a relatively straight reach of channel. The slope-conveyance method is used primarily for shaping and extending rating curves, whereas the slope-area method is used for specific floods. The step-backwater method, also based on the Manning equation, requires more cross-section data than the slope-area ethod, but has a water-surface profile convergence characteristic that negates the need for known or estimated water-surface slope. Uncertainties in calculating peak discharge for historical floods may be quite large. Various investigations have shown that errors in calculating peak discharges by the slope-area method under ideal conditions for recent floods (i.e., when flood elevations, slope and channel characteristics are reasonably certain), may be on the order of 10-25%. Under less than ideal conditions, where streams are hydraulically steep and rough, errors may be much larger. The additional uncertainties for historical floods created by the passage of time may result in even larger errors of peak discharge. ?? 1987.