This paper investigates the modeling of creep deformation of grade 91 steel under high temperatures. This type of ferritic/martensitic steel is used as a reference when designing components intended to resist creep at elevated temperatures such as pressure vessels in sodium fast reactors (SFR). Those components have an intended life span of 60 years and no experimental creep data is available for such period. Thus, understanding the mechanism of creeps of the grade 91 steel is crucial, as simple extrapolation of experimental data may yield an overestimated design lifespan. This paper adopts a continuum mechanics approach where the grade 91 is simulated using mechanism-based microstructural evolution constitutive laws. Two main mechanisms are considered: one when the applied stress is low and the creep is diffusion based, and the other at high stresses where the dislocation glide and climb dominate the creep behavior. These constitutive models will be tested on a polycrystalline microstructural model to investigate stresses at the grains and the grain-boundaries compared to the remote applied stress.