Tadpoles are unusual among vertebrates in having a globose body with a laterally compressed tail abruptly appended to it. Compared with most teleost fishes, tadpoles swim awkwardly, with waves of relatively high amplitude at both the snout and tail tip. In the present study, we analyze tadpole propulsion using a three-dimensional (3D) computational fluid dynamic (CFD) model of undulatory locomotion that simulates viscous and unsteady flow around an oscillating body of arbitrary 3D geometry. We first confirm results from a previous two-dimensional (2D) study, which suggested that the characteristic shape of tadpoles was closely matched to their unusual kinematics. Specifically, our 3D results reveal that the shape and kinematics of tadpoles collectively produce a small 'dead water' zone between the head-body and tail during swimming precisely where tadpoles can and do grow hind limbs--without those limbs obstructing flow. We next use our CFD model to show that 3D hydrodynamic effects (cross flows) are largely constrained to a small region along the edge of the tail fin. Although this 3D study confirms most of the results of the 2D study, it shows that propulsive (Froude) efficiency for tadpoles is overall lower than predicted from a 2D analysis. This low efficiency is not, however, a result of the high-amplitude undulations of the tadpole. This was demonstrated by forcing our 'virtual' tadpole to swim with fish-like kinematics, i.e. with lower-amplitude propulsive waves. That particular simulation yielded a much lower Froude efficiency, confirming that the large-amplitude lateral oscillations of the tadpole do, indeed, provide positive thrust. This, we believe, is the first time that the unsteady flow generated by an undulating vertebrate has been realistically modelled in three dimensions. Our study demonstrates the feasibility of using 3D CFD methods to model the locomotion of other undulatory organisms.