Mathematical modeling of stress generation in casting processes is a d
ifficult, complex subject that is now receiving increased attention. T
his paper reviews the basic equations, solution methods and important
phenomena associated with casting processes that require special numer
ical treatment. Stress modeling begins with a coupled, transient heat
transfer analysis, including solidification, shrinkage-dependent inter
facial heat transfer, and fluid flow effects. Further complicating phe
nomena include phase transformations, temperature, stress and structur
e-dependent plastic-creep, interaction between the casting and the mol
d, hydrostatic pressure from the liquid, the effects of fluid flow, an
d crack formation. Computational issues include numerical methods for
handling these phenomena, mesh refinement, and two-dimensional stress
state. Example applications are presented for the thermal-mechanical b
ehavior of the solidifying steel shell in the mold region of a continu
ous slab easter, using a finite-element model, which accounts for many
of these phenomena.