Although underwater vehicles often operate in time-varying, nonuniform currents, the effect of flow gradients on vehicle dynamics is typically ignored in motion models used for control and estimation. Forces and moments due to a nonuniform flow field are strongest when apparent mass effects are important and flight paths are most sensitive to these disturbances when flow-relative velocities are small – precisely the situation for underwater gliders. This paper presents a nonlinear multi-body dynamic model for an underwater glider operating in an unsteady, nonuniform flow. The eight degree of freedom model incorporates a cylindrically actuated moving mass, a common glider actuation scheme. To illustrate the utility of this full dynamic model, numerical motion predictions are compared with those of simpler models for a variety of nonuniform flow fields. We also demonstrate the use of the full dynamic model for flow estimation using parameter adaptive filtering.