Many important insights into the dynamic coupling among climate, erosion, and tectonics in mountain areas have derived from several numerical models of the past few decades which include descriptions of bedrock incision. However, many questions regarding incision processes and morphology of bedrock streams still remain unanswered. A more mechanistically based incision model is needed as a component to study landscape evolution. Major bedrock incision processes include (among other mechanisms) abrasion by bed load, plucking, and macroabrasion (a process of fracturing of the bedrock into pluckable sizes mediated by particle impacts). The purpose of this paper is to develop a physically based model of bedrock incision that includes all three processes mentioned above. To build the model, we start by developing a theory of abrasion, plucking, and macroabrasion mechanisms. We then incorporate hydrology, the evaluation of boundary shear stress, capacity transport, an entrainment relation for pluckable particles, a routing model linking in-stream sediment and hillslopes, a formulation for alluvial channel coverage, a channel width relation, Hack's law, and Exner equation into the model so that we can simulate the evolution of bedrock channels. The model successfully simulates various features of bed elevation profiles of natural bedrock rivers under a variety of input or boundary conditions. The results also illustrate 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 may be an integral part of normal incision processes. The model is expected to improve the current understanding of the linkage among physically meaningful input parameters, the physics of incision process, and morphological changes in bedrock streams.