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Existing analytical models, which have assumed a fully‐penetrating stream (FPS), give significant error in predicting stream depletion/filtration rate (SDR) for the typical case of a partially‐penetrating stream. In addition, existing source terms, embedded in flow equations for stream treatment, neglect the effect of small‐scale streambed storage. This study develops two new models for describing three‐dimensional (3D) flow in a pumped confined aquifer connected to a stream with shallow penetration. One model treats a finite‐width stream as a modified source term reflecting the streambed storage effect for the case of near‐stream groundwater extraction. The finite element solution of the model is built. The other model considers a rectilinear stream as a source term neglecting the streambed storage effect for the case of far‐from‐stream groundwater extraction. The semi‐analytical solution of the model is derived by the Laplace transform and Fourier transform. The time‐domain approximate solution for SDR is also derived. Results suggest the modified source term serves as a convenient and efficient alternative to existing stream treatments in incorporating the streambed storage effect and achieving both accurate solution prediction and coarse aquifer discretization. Sensitivity analysis demonstrates the response of SDR more sensitive to the change in vertical aquifer hydraulic conductivity than that in horizontal one due to shallow penetration of stream. A shallow stream can be regarded as a FPS in predicting SDR under three quantitative conditions. As concluded, this study provides hydrologists with a better understanding of SDR behavior subject to 3D flow in typical stream‐aquifer system.

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