Channel incision into bedrock by abrasion plays an important role in orogenesis by redistributing material within drainage basins. It is often the dominant erosional mechanism in bedrock streams. The purpose of this paper is to qualitatively apply a physically-based incision model of abrasion to bedrock streams in western Kaua'i. These streams have various long profiles despite their homogeneous lithology throughout.We begin by analytically and numerically developing a physically-based bedrock incision model by abrasion (wear) driven by collision that includes a cover factor for alluvial deposits, the capacity bedload transport rate of effective tools, sediment delivery from hillslopes, and hydrology.The numerical results in the present study are analyzed together with Digital Elevation Model data of stream longitudinal profiles and field observations due to DeYoung (2000) and Seidl et al. (1994). The model qualitatively simulates the main features of the bedrock rivers in western Kaua'i, most of which have profiles with a convex shape, a straight shape, or with knickpoints. The results support an analytical result that knickpoints found in bedrock rivers may be autogenic in addition to being driven by base level fall and lithologic changes. This supports the concept that bedrock incision by knickpoint migration might not be separate from the normal abrasion process. Moreover, the results show that the upstream distance from a channel head to its divide is an important factor affecting the shape of the long profile of a bedrock river. The distance to channel head of the streams flowing into the Mana Plain region of Kaua'i was reduced as Waimea Canyon migrated upstream and captured their headwaters. This reduction in channel head region, combined with a relative sea level fall of 10m over the last 5000 years, may have played a role in the formation of the Mana Plain itself. In the Napali region just north of the Mana Plain, on the other hand, where there is no limit on the upstream distance from the channel head to the divide, all streams show distinct long profiles with knickpoints which may have developed both autogenically and due to base level fall.