Hot isostatic pressing of metal powders involves a complex thermal and mechanical coupling process. A constitutive model based on Perzyna's elastic-viscoplasticity equation was proposed, and a Lagrangian finite element method was applied to analyze the large deformation, nonlinear friction, powder flow, and densification behavior during hot isostatic pressing. The mechanical behavior of the powders was analyzed in terms of stress distribution. For comparison to the simulation results, the density, shape deformation, and residual stress of the specimens were evaluated using Archimedes' principle, 3D measuring technology, and Empyrean X-ray diffractometer.