In this paper a three-dimensional (3-D) front-tracking (FT) model is presented featuring a new method to evaluate the surface force model that circumvents the explicit computation of the interface curvature. This method is based on a direct calculation of the net tensile forces acting on a differential element of the interface. Our model can handle a large density and viscosity ratio and a large value of the surface tension coefficient characteristic for gas-liquid systems. First, the results of a number of test cases are presented to assess the correctness of the implementation of the interface advection and remeshing algorithms and the surface tension model. Subsequently, the computed terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace. In addition drag coefficients for rising air bubbles in water were successfully computed, a system that has proven difficult to simulate by other methods, and showed good agreement with existing correlations. Finally, a number of sample calculations involving multiple bubbles are reported to demonstrate the capabilities of our three-dimensional FT model.