In this study, numerical analysis has been performed to clarify the assessment of volume tracking algorithms in a three-dimensional flow field dominated by surface tension. The FLAIR method has been extended to three-dimensional problems in this study. The distinct feature of FLAIR developed in two-dimension is that the slope of line segment is estimated based only on two neighboring volume fractions. This feature is also adopted in the three-dimensional FLAIR method proposed in this study, even if the three-dimensional slope of interface is neglected. This three-dimensional FLAIR is applied to a non-straining flow field and a surface tension dominated flow field. The results are compared with those of the donor-acceptor method, the SURFER method and the CIP method with digitization. Consequently, it has been found that the precision of translation of interface is much more improved by the use of the CIP method with digitization and the three-dimensional FLAIR method than that of the other methods. However, the CIP method with digitization will produce an uneven interface.