Plasma-material interaction is a major concern in fusion reactor design and analysis. The Material Plasma Exposure eXperiment (MPEX) will explore plasma-material interaction under fusion reactor plasma conditions. Samples with accumulated displacement damage (characterized by displacements per atom) produced by fast neutron irradiations in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory will be studied in the MPEX facility. This paper presents assessments of the calculated induced radioactivity and resulting radiation dose rates of a variety of potential fusion reactor plasma-facing materials, e.g., tungsten. The scientific code packages Monte Carlo N-Particle (MCNP) and Standardized Computer Analyses for Licensing Evaluation (SCALE) were used to simulate irradiation of the samples in HFIR. This included the generation and depletion of nuclides in the material and the subsequent composition, activity levels, gamma radiation fields, and resultant dose rates as a function of cooling time. A challenge of the MPEX project is to minimize the radioactive inventory in the preparation of the samples and the sample dose rates for inclusion in the MPEX facility.