Detailed information concerning the rate and particle size distribution of bed material transport by streamflows can be very difficult and expensive to obtain, especially where peak streamflows are brief and bed material is poorly sorted, including some very large boulders. Such streams, however, are common in steep, arid watersheds. Any computational approach must consider that (1) only the smaller particle sizes present on the streambed move even during large floods and (2) the largest bed particles exert a significant form drag on the flow. Conventional methods that rely on a single particle size to estimate the skin friction shear stress acting on the mobile fraction of the bed material perform poorly. Instead, for this study, the skin friction shear stress was calculated for the observed range of streamflows by calculating the form drag exerted on the reach‐averaged flow field by all particle sizes. Suspended and bed load transported rates computed from reach‐averaged skin friction shear stress are in excellent agreement with measured transport rates. The computed mean annual bed material load, including both bed load and suspended load, of the East Fork Virgin River for the water years 1992‐1996 was approximately 1.3×10 ⁵ t. A large portion of the bed material load consists of sand‐sized particles, 0.062–1.0 mm in diameter, that are transported in suspension. Such particles, however, constituted only 10% of the surface bed material and less than 25% of the subsurface bed material. The mean annual quantity of bed load transported was 1060 t/yr with a median size of 15 mm.