In order to address how emergy cycles with material in systems, the following work uses three studies that 1) explores the reasons why emergy should follow cycles, 2) shows how emergy should be allocated to cycling material within a system, and 3) shows how emergy can be simulated dynamically in systems that cycle material. The first study investigated how waste flows from its production process, through some transformation in a treatment system, and into the environment, which must use resources to absorb the waste's residual available energy that went untreated by the treatment system. This study showed that much work was required by the environment to return constituents in waste to background levels. Waste treatment systems for two different wastewater types and three different scenarios of treatment were compared using this new methodology and a novel index. Passive treatment systems performed better with regards to the new index, using less purchased emergy and more renewable emergy. The second study examined how emergy can be allocated to cycles within systems that have internal material flows as a large component (i.e., forest ecosystem and farms). Three study sites were evaluated that cycled phosphorus at similar levels internally. The natural system recycled the same amount of mass but required less emergy to do so because purchased emergy was not required for the forest to recycled emergy. In the farms, NPP of crops, and thus recycling phosphorus, required substantial purchased inputs. The third study adapted a previous minimodel with two storages of material, one low quality and one higher quality. The low quality material storage was open to material input and output and the overall system was open to energy input and output. Response variables of this model were compared to the previous model and to previous rules for simulating dynamics of emergy cycles within systems. This model showed that a system open to material inputs and outputs could accumulate more material while proportionately less emergy flows in. Consequently, emergy becomes "diluted" by increased material accumulation in systems that are open to material as those closed to material have higher steady state emergy cycling.