a b s t r a c tA number of surface tension models have been implemented in a 3D multi-physics multi-material code, ALE-AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE-AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. Based on the results, the height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.