A model is presented which accounts for the formation of coronal magne
tic field lines with the appropriate ''dipped'' structure to support p
rominences. The critical ingredients of the model are that the promine
nce magnetic field is a truly three-dimensional structure with signifi
cant variation along the prominence length, and the magnetic field is
strongly sheared near the photospheric neutral line. Numerical calcula
tions are presented which demonstrate that these two features lead to
dip formation. In addition our model is able to account for the long-p
uzzling observation of inverse polarity in quiescent prominences.