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Abstract: The current available g-functions obtained from the moving finite line source (MFLS) model for design and simulation of vertical borehole heat exchangers (BHEs) neglects the effects of buried depth, i.e. the vertical distance between the ground surface and the BHEs. This study proposed a new analytical solution of the MFLS model in a single integral form that extends the validity of the MFLS model by taking the effects of buried depth into consideration. Furthermore, the spatial superposition technique was employed in computing new g-functions using the new proposed analytical solution for multiple borehole field. A customized MATLAB code was deployed to compute the new proposed solution and the new g-functions. The correctness of them was numerically verified with an equivalent three-dimensional (3D) finite-element (FE) model developed in COMSOL Multiphysics software. A sensitivity study was carried out to investigate the influence of the buried depth. Results reveal that the new proposed solution must be used over the standard MFLS model to consider the combined effects of buried depth and groundwater flow when calculating the temperature variation of the Peclet number (Pe) < 22. The findings also indicate that the effects of buried depth increase as the borehole length decreases, and the effect of buried depth is more significant in a borehole field containing multiple boreholes due to the accumulation effects of the buried borehole. Neglecting buried depth could result in an under-estimation of the temperature variation by more than 8%. Therefore, the buried depth becomes an important parameter in the design of BHEs.