The rheology of oceanic lithosphere is important to our understanding of mantle dynamics and to the emergence and manifestations of plate tectonics. Data from experimental rock mechanics suggest rheology is dominated by three different deformation mechanisms including frictional sliding, low‐temperature plasticity, and high‐temperature creep, from shallow depths at relatively cold temperatures to large depths at relatively high temperatures. However, low‐temperature plasticity is poorly understood. This study further constrains low‐temperature plasticity by comparing observations of flexure at the Hawaiian Islands to predictions from 3‐D viscoelastic loading models with a realistic lithospheric rheology of frictional sliding, low‐temperature plasticity, and high‐temperature creep. We find that previously untested flow laws significantly underpredict the amplitude and overpredict the wavelength of flexure at Hawaii. These flow laws can, however, reproduce observations if they are weakened by a modest reduction (25–40%) in the plastic activation energy. Lithospheric rheology is strongly temperature dependent, and so we explore uncertainties in the thermal structure with different conductive cooling models and convection simulations of plume‐lithosphere interactions. Convection simulations show that thermal erosion from a plume only perturbs the lithospheric temperature significantly at large depths so that when it is added to the thermal structure, it produces a small increase in deflection. In addition, defining the temperature profile by the cooling plate model produces only modest weakening relative to the cooling half‐space model. Therefore, variation of the thermal structure does not appear to be a viable means of bringing laboratory‐derived flow laws for low‐temperature plasticity into agreement with geophysical field observations and modeling. Plain Language Summary Volcanic eruptions continually build the Hawaiian Island chain. The islands impose stresses on the Pacific plate that bends in response to their weight. The degree to which the plate bends is controlled by the plate's strength. The strength of tectonic plates on Earth has implications for the long‐term evolution of the entire planet. We are thus motivated to constrain the strength of the Pacific plate by comparing observations of the flexure of the top of ocean crust to predictions from computer simulations. The computer simulations incorporate flow laws from laboratory experiments on constituent minerals. We find that laboratory‐derived flow laws underpredict the flexure and hence overpredict the strength of the plate. The flow laws make predictions consistent with observations, however, if we apply a modest variation to the sensitivity to changes in temperature. Meanwhile, the source of volcanic activity at Hawaii is a mantle plume composed of buoyant material that flows from the core‐mantle boundary to the surface. We test whether the plume significantly warms and erodes the plate. A plume only effects the deepest part of the plate, while the shallower portion of the plate remains strong and so has little impact on the flexure.