This paper introduces a flexible framework for conceptual hydrological modeling, with two related objectives: (1) generalize and systematize the currently fragmented field of conceptual models and (2) provide a robust platform for understanding and modeling hydrological systems. In contrast to currently dominant "fixed" model applications, the flexible framework proposed here allows the hydrologist to hypothesize, build, and test different model structures using combinations of generic components. This is particularly useful for conceptual modeling at the catchment scale, where limitations in process understanding and data availability remain major research and operational challenges. The formulation of the model architecture and individual components to represent distinct aspects of catchment-scale function, such as storage, release, and transmission of water, is discussed. Several numerical strategies for implementing the model equations within a computationally robust framework are also presented. In the companion paper, the potential of the flexible framework is examined with respect to supporting more systematic and stringent hypothesis testing, for characterizing catchment diversity, and, more generally, for aiding progress toward more unified hydrological theory at the catchment scale.