At present, the available Ramberg–Osgood (R–O) parameters for different metals (e.g., in ASME code and other literatures) are static (generally based on a tensile curve). These static R–O parameters cannot accurately model the cyclic plasticity behavior. This work presents the cyclic R–O material hardening parameters for 316 stainless steel similar metal welds. The parameters were estimated under various conditions (in-air at room temperature, 300 °C in-air, and in-air at primary water conditions for a pressurized water reactor (PWR)). It is anticipated that the reported results would be useful for computational mechanics-based shakedown analysis and fatigue life estimation of PWR components.