South of Australia, the monthly mean wind stress curl is positive during both summer and winter and leads to Ekman pumping and downwelling throughout the region. Sverdrup dynamics indicates that this downwelling should lead to a northward transport of around 5--10 Sv (1 Sv = 10 m3 s-1). Classical arguments for western boundary currents are adapted to show that this transport should be deflected into an upwelling favorable boundary current that flows from east to west along Australia's southern shelves: the Flinders Current. Support for this proposition is obtained from results of the Ocean Circulation and Climate Advanced Modelling project (OCCAM), Sverdrup transports, and limited observations for the region. In addition, the OCCAM results show that the northward transport leads to upwelling at depths below 400 m and that the Flinders Current (1) intensifies from Victoria to Western Australia (transport ~8 Sv with speeds up to 15 cm s-1), (2) can extend from the surface to depths of 800 m, and (3) is found during both summer and winter. During winter the winds are downwelling favorable and lead to a coastal current that flows from west to east and opposes the Flinders Current. Further support for the origin and nature of the Flinders Current is obtained from simple numerical experiments made using a rectangular domain and idealized representations of the summer and winter wind stress.