An asymptotic model is developed for the problem of slab casting. The
model assumes that the slab is thin and uses two-dimensional planar fl
ow and deformation for simplicity. The governing equations are present
ed, and a reduced set of equations are derived from the asymptotic for
mulation. Three features are included in the present analysis: treatme
nt of the thermal transport, inclusion of the solidification front dev
elopment and calculation of the components of the dilatation.