Monte Carlo dose calculation is currently the most accurate algorithm, but it is still too computationally intensive and slow to be used routinely in clinics. An implementation of the Linear Boltzmann Transport Equation, Acuros XB dose calculation algorithm, has similar accuracy to Monte Carlo but is much faster, and has already been used in many clinics. Like Monte Carlo, Acuros allows the user to report dose to water or dose to medium. The main aim of this study is to compare and evaluate both Acuros XB dose-to-medium Dm,m and dose-to-water Dw,m algorithms with the widely used AAA algorithm. Twenty one lung patients that previously received IMRT or VMAT treatments at our institution were analysed by recalculating plans for each one with AAA algorithm (reviewed and approved by our radiation oncologists) and with both reporting modes of Acuros XB algorithm. All plans used the same monitor units (MU) and 2.5 mm grid size. For each patient, D100 of gross tumor volume (GTV) in each plan were compared and dose distributions calculated by AAA, Acuros Dw,m and Acuros Dm,m were visually compared as well. Difference between D100 of GTV calculated by AAA and Acuros XB Dm,m are larger than the differences between AAA and Acuros XB Dw,m for all patients. When D100 of GTV is evaluated, the largest difference between AAA and Acuros XB is 12.8%, and between AAA and Acuros XB DC is 2.5%. For 10 out of 21 patients, D100 differences between AAA and Acuros XB Dm,m are more than 4%. In addition, doses calculated by Acuros XB Dm,m are always lower than the doses calculated by AAA inside the GTV. In general, Acuros XB Dw,m dose are bit lower than AAA but higher than Acuros XB Dm,m except for one patient. When visually comparing the dose distributions, the difference between AAA and Acuros Dm,m is larger than the difference between AAA and Acuros XB Dw,m. The results show that the differences in dose calculated by AAA and Acuros Dm,m are larger than the dose differences between AAA and Acuros Dw,m. Moreover, there is a systematic difference between AAA and Acuros Dm,m and it will cause significant discrepancies if both AAA and Acuros Dm,m are used in clinical trials. In some cases, in order to meet protocol dose goals, the dose to a plan reported in Acuros Dm,m may have to be increased more than 10% compared to the same plan reported with AAA. This study indicates that Acuros Dw,m should be used, however, this contradicts current recommendations in literature. Hence, further investigation and clarification are needed about which dose reporting mode should be used.