Based on previous research, we developed and successfully tested a new linear iterative refinement method to rapidly simulate borehole nuclear measurements acquired in vertical wells. The approximation considers 2D spatial properties of Monte Carlo-derived flux-sensitivity functions (FSFs) to simulate neutron and density measurements. Based on new research, we implemented the linear iterative refinement method with explicit 3D spatial properties of FSFs to approximate nuclear borehole measurements acquired in high-angle and horizontal (HA/HZ) wells. We used generic neutron and density tools that are close to commercial tool designs to construct 3D FSFs in the proximity of a bed boundary between layers of contrasting petrophysical properties. Likewise, to benchmark the approximation, we consider adjacent layers of 5% and 30% porosity water-saturated sandstone. For the case of neutron measurements, variations of azimuthal geometric factors are as large as 20° and 57° for the near and far detectors, respectively. Variations in the radial length of investigation (J-factors) are as large as for near and far detectors. In the case of density measurements, radial and azimuthal geometric factors are approximately invariant. Linear iterative refinement approximations yield errors in the simulated neutron porosity ranging from 1.6% to 4.3% with respect to Monte Carlo-simulated logs in wells deviating from 60° to 85° from the vertical.