This paper presents a 1-dimensional numerical model for the morphodynamic evolution of the bed elevation along a simple river channel network consisting of a main stem and two tributaries. The purpose of the model is to represent the evolution of the sand-bed portion of the Fly/Strickland River System, Papua New Guinea, in response to sea level rise since the last glacial maximum. The model differs from most existing 1-D bed evolution models in that the channel cross-sectional geometry is allowed to vary over time in response to changes in sediment supply or bed elevation such that the Shields parameter at bankfull discharge is held constant. The model is driven by boundary conditions for sediment discharge at the upstream end of each tributary and by a water surface elevation boundary condition at the downstream end of the main stem. It predicts significant adjustment in the longitudinal profiles of both the larger and smaller tributaries (the Strickland and Middle Fly Rivers, respectively) as the downstream main stem (the Lower Fly River) aggrades in response to sea level rise.