Hastelloy X (HX) and 304 stainless steel (304SS) are widely used in the pressure vessel and piping industries, specifically in nuclear and chemical reactors, pipe, and valve applications. Both alloys are favored for their resistance to extreme environments, although the materials exhibit a rate-dependent mechanical behavior. Numerous unified viscoplastic models proposed in literature claim to have the ability to describe the inelastic behavior of these alloys subjected to a variety of boundary conditions; however, typically limited experimental data are used to validate these claims. In this paper, two unified viscoplastic models (Miller and Walker) are experimentally validated for HX subjected to creep and 304SS subjected to strain-controlled low cycle fatigue (LCF). Both constitutive models are coded into ansys Mechanical as user-programmable features. Creep and fatigue behavior are simulated at a broad range of stress levels. The results are compared to an exhaustive database of experimental data to fully validate the capabilities and performance of these models. Material constants are calculated using the recently developed Material Constant Heuristic Optimizer (macho) software. This software uses the simulated annealing algorithm to determine the optimal material constants through the comparison of simulations to a database of experimental data. A qualitative and quantitative discussion is presented to determine the most suitable model to predict the behavior of HX and 304SS.