Fluid mechanics of Taylor bubbles and slug flows is investigated in vertical, circular channels using detailed, three-dimensional computational fluid dynamics simulations. The Volume of Fluid model with the interface-sharpening algorithm, implemented in the commercial CFX4 code, is used to predict the shape and velocity of Taylor bubbles moving along a vertical channel. Several cases are investigated, including both a single Taylor bubble and a train of bubbles rising in water. It is shown that the potential flow solution underpredicts the water film thickness around Taylor bubbles. Furthermore, the computer simulations that are performed reveal the importance of properly modeling the three-dimensional nature of phenomena governing the motion of Taylor bubbles. Based on the present results, a new formula for the evaluation of bubble shape is derived. Both the shape of Taylor bubbles and the bubble rise velocity predicted by the proposed model agree well with experimental observations. Furthermore, the present model shows good promise in predicting the coalescence of Taylor bubbles.