A semi-analytical method based on the finite line source (FLS) solution is presented to evaluate thermal response factors for geothermal bore fields with mixed series and parallel connections between boreholes. Each borehole in the bore field is modelled as a series of finite line source segments. The spatial and temporal superposition of the FLS solution for all pairs of segments in the bore field gives the total temperature change at the wall of the borehole segments. The axial variation of heat extraction rates is evaluated from the borehole wall temperatures using a steady-state analytical model of the fluid temperature variations inside the boreholes, considering the piping configuration to determine the inlet fluid temperature into a borehole from the inlet fluid temperature into the bore field. The concept of effective bore field thermal resistance is introduced to relate the arithmetic mean fluid temperature in a bore field, the average heat extraction rate per unit borehole length and a newly introduced effective borehole wall temperature. The g-function of a bore field with mixed series and parallel connections between boreholes is then defined from the effective borehole wall temperature, rather than the average borehole wall temperature.