In this paper, the accuracy of dose planning calculations for boron neutron capture therapy (BNCT) of brain and head and neck cancer was studied at the FiR 1 epithermal neutron beam. A cylindrical water phantom and an anthropomorphic head phantom were applied with two beam aperture-to-surface distances (ASD). The calculations using the simulation environment for radiation application (SERA) treatment planning system were compared to neutron activation measurements with Au and Mn foils, photon dose measurements with an ionization chamber and the reference simulations with the MCNP5 code. Photon dose calculations using SERA differ from the ionization chamber measurements by 2-13% (disagreement increased along the depth in the phantom), but are in agreement with the MCNP5 calculations within 2%. The 55Mn(n,γ) and 197Au(n, γ) reaction rates calculated using SERA agree within 10% and 8%, respectively, with the measurements and within 5% with the MCNP5 calculations at depths >0.5 cm from the phantom surface. The 55Mn(n,γ) reaction rate represents the nitrogen and boron depth dose within 1%. Discrepancy in the SERA fast neutron dose calculation (of up to 37%) is corrected if the biased fast neutron dose calculation option is not applied. Reduced voxel cell size (≤0.5 cm) improves the SERA calculation accuracy on the phantom surface. Despite the slight overestimation of the epithermal neutrons and underestimation of the thermal neutrons in the beam model, neutron calculation accuracy with the SERA system is sufficient for reliable BNCT treatment planning with the two studied treatment distances. The discrepancy between measured and calculated photon dose remains unsatisfactorily high for depths >6 cm from the phantom surface. Increasing discrepancy along the phantom depth is expected to be caused by the inaccurately determined effective point of the ionization chamber.