Various analytical, semi-analytical, and empirical models have been proposed to characterize rate and pressure behavior as a function of time in tight gas and shale gas systems featuring horizontal wells with multiple hydraulic fractures. Despite a few analytical models, as well as a small number of published numerical studies, there is currently little consensus regarding the large-scale flow behavior over time in such systems, particularly regarding the dominant flow regimes and whether or not reservoir properties or volumes can be estimated from well performance data. We constructed a fit-for-purpose numerical simulator which accounts for a variety of production features pertinent to these systems—specifically ultra-tight matrix permeability, hydraulically fractured horizontal wells with induced fractures of various configurations, multiple porosity and permeability fields, and desorption. These features cover the production mechanisms which are currently believed to be most relevant in tight gas and shale gas systems. We employ the numerical simulator to examine various tight gas and shale gas systems and to identify and illustrate the various flow regimes which progressively occur over time. We perform this study at fine grid discretization on the order of 1 mm near fractures to accurately capture flow effects at all time periods. We visualize the flow regimes using specialized plots of rate and pressure functions, as well as maps of pressure and sorption distributions. We use pressure maps to visualize the various flow regimes and their transitions in tight gas systems. In a typical tight gas system, we illustrate the initial linear flow into the hydraulic fractures (i.e., formation linear flow), transitioning to compound formation linear flow, and eventually transforming into elliptical flow. We explore variations of possible shale gas system models. Based on diffusive flow (with and without desorption), we show that due to the extremely low permeability of shale matrix (a few nanodarcies), the flow behavior is dominated by the extent of and configuration of the fractures. This work expands our understanding of flow behavior in tight gas and shale gas systems, where such an understanding may ultimately be used to estimate reservoir properties and reserves in these types of reservoirs.