The stagnant zones in nested flow systems have been assumed to be critical to accumulation of transported matter, such as metallic ions and hydrocarbons in drainage basins. However, little quantitative research has been devoted to prove this assumption. In this paper, the transport of age mass is used as an example to demonstrate that transported matter could accumulate around stagnation points. The spatial distribution of model age is analyzed in a series of drainage basins of different depths. We found that groundwater age has a local or regional maximum value around each stagnation point, which proves the accumulation of age mass. In basins where local, intermediate and regional flow systems are all well developed, the regional maximum groundwater age occurs at the regional stagnation point below the basin valley. This can be attributed to the long travel distances of regional flow systems as well as stagnancy of the water. However, when local flow systems dominate, the maximum groundwater age in the basin can be located around the local stagnation points due to stagnancy, which are far away from the basin valley. A case study is presented to illustrate groundwater flow and age in the Ordos Plateau, northwestern China. The accumulation of age mass around stagnation points is confirmed by tracer age determined by 14C dating in two boreholes and simulated age near local stagnation points under different dispersivities. The results will help shed light on the relationship between groundwater flow and distributions of groundwater age, hydrochemistry, mineral resources, and hydrocarbons in drainage basins.