Ray geometry, travel time, and spreading loss are examined for a moving medium. The sound speed and current are both depth‐variable, and the current direction is fixed in space. For a linear sound speed and current, ray geometry is investigated and an approximate solution is obtained which leads to helical paths. For a bottom‐mounted source and receiver in the vertical plane of the current, the linear model is used to investigate ray geometry, travel time, spreading loss, and the acoustic field associated with refracted/bottom‐reflected (RBR) transmissions. It is shown that the effects of current gradients and bottom currents on the phase and amplitude of the acoustic field are important and cannot be ignored. Further, long‐term time variations in the current gradient are shown to cause much shorter‐term variations in phase and amplitude.