In-stream sediment mining and feeding inevitably change the sediment budget of an alluvial river, and may substantially alter its hydraulics and morphology. These alterations can have variable effects on fluvial habitat. Minimization of the detrimental effects and maximization of the beneficial impacts require a quantitative understanding of the complicated interaction between flow, sediment transport and morphological evolution. However, existing numerical river models have been developed for purely natural fluvial processes, and are rarely, if ever, applicable where interactive sediment mining and feeding take place. This paper presents numerical models for alluvial rivers subject to interactive sediment mining and feeding, within the context of shallow water hydrodynamics. The theoretical framework of two-and one-dimensional models is provided from conservation laws, and closure requirements are briefly addressed. The present models are distinguished from previous ones because of the complete continuity equations for the water and sediment phases and bed material, which are scrutinized under idealized scenarios with known analytical features. The continuity equations contain terms arising from mass exchange, which, though less known to the majority of fluvial hydraulics community, may be significant not only scientifically but also under regimes of practical interests. To demonstrate the applicability of the present models, a numerical study is provided on the dynamics of an otherwise aggrading channel in response to sediment mining, showing the role of sediment mining in mitigating river aggradation.