Several alloy systems are susceptible to weld hot cracking. Weld hot cracking occurs by fracture of liquid films, normally grain boundary liquid films, at the late stage of the solidification of the weld. The cracks can be small and therefore difficult to detect by nondestructive test methods. If hot cracks are not repaired, they can act as sites for initiation of fatigue and stress corrosion cracking, which in turn can lead to catastrophic failure in critical applications such as aerospace engines and nuclear power plants. Therefore, it is of highest importance to design weld processes so that hot cracking can be avoided. Here, numerical simulation can be a powerful tool for optimizing weld speed, heat input, weld path geometry, weld path sequences, weld fixturing, etc., such that the risk for hot cracking can be minimized. In this thesis, we propose a modeling approach for simulating weld hot cracking in sheet metals with low welding speeds and fully penetrating welds. These conditions are assumed to give rise to isolated grain boundary liquid films (GBLFs) whose crack susceptibility can be analyzed using one-dimensional models. The work is divided into four journal papers. The three first papers treat hot cracking that occurs in the fusion zone of the weld while the last paper treats hot cracking in the partially melted zone of the weld. The main content of the four papers are summarized below. In paper A, a pore-based crack criterion for hot cracking has been developed. This criterion states that cracking occurs in a GBLF if the liquid pressure in the film goes below a fracture pressure. The fracture pressure is determined from a pore model as the liquid pressure that is required to balance the surface tension of an axisymmetric pore in a liquid film located between two parallel plates at a given critical pore radius. The fracture pressure depends on the surface tension, the spacing between the parallel plates and the gas concentration in the liquid. In order to evaluate the above pore-based crack criterion in a GBLF the liquid pressure in the film most be known. In paper B, a one-dimensional GBLF pressure model for a columnar dendritic microstructure has been developed. This model is based on a combination of Poiseuille parallel plate flow and Darcy porous flow. Flow induced by mechanical straining of the GBLF is accounted for by a macroscopic mechanical strain field that is localized to the GBLF by a temperature dependent length scale. In paper C, a computational welding mechanics model for a Varestraint test is developed. The model is used to calibrate the crack criterion in paper A and the pressure model in paper B. It is then used to test the crack criterion in Varestraint tests with different augmented strains. Calculated crack locations, orientations, and widths are shown to correlate well to the experimental Varestraint tests. vii Finally, in paper D, a segregation model for predicting the thickness of eutectic bands has been developed. The thickness of eutectic bands affects the degree of liquation in partially melted zone, and therefore is an important factor for hot cracking in this region of the weld.