The Material Plasma Exposure eXperiment (MPEX) steady-state linear plasma facility is currently under design at Oak Ridge National Laboratory to expose target specimens to fusion divertor regimes. The neutron-irradiated target is actively cooled and remote handled in the MPEX facility for conducting plasma-material–interaction (PMI) experiments. In this study, the steady-state stresses in the target and target assembly system are investigated using two-dimensional (2-D) and three-dimensional (3-D) models to provide expected stresses/strains under the heat loads to which various system components would be exposed during MPEX operation. The calculated temperatures from the 2-D axisymmetric mechanical model were found to be in excellent agreement with those from the full 3-D thermohydraulic model, providing a strong model validation. Numerical simulation results for the steady-state mechanical model indicate nonuniform distributions for the temperature, stress, and deformation within the critical components. For the initial design, the deformation results indicate possible gap openings between contacting surfaces below the plasma-facing materials. To reduce the possibility of interfacial gap opening, the target assembly was slightly changed and evaluated using the 2-D stress model. Numerical simulation results indicate that the interfacial gap openings can be minimized without drastically changing the entire target assembly. The stress-strain conditions for the target will be further used to assess the appropriate operation during MPEX experiments and gain insight into materials science phenomena during PMI.