We present a new semi-analytical flow and transport model for the simulation of 3D steady-state flow and particle movement between groundwater, a surface water body and a radial collector well in geometrically complex unconfined aquifers. This precise and grid-free Series Solution-analytic element method approach handles the irregular configurations of radial wells more efficiently than grid-based methods. This method is then used to explore how pumping well location and river shape interact and together influence (1) transit time distribution (TTD) of captured water in a radial collector well and TTD of groundwater discharged into the river and (2) the percentage of well waters captured from different sources. Results show that meandering river shape plays a significant role in controlling the aforementioned metrics and that increasing the pumping rate has different consequences in different situations. This approach can also inform the design of water remediation and groundwater protection systems (e.g., river bank filtration and well head protection area).