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Abstract One of the essential characteristics of earthquakes associated with large tsunami generation is the depletion of high‐frequency radiation, which is not well understood by elastic dislocation theory and largely not accounted for in most rupture models of real events. We present fully coupled models of dynamic rupture, ocean acoustic waves, and tsunami for the 1896 Sanriku earthquake with wedge inelasticity. The inelastic wedge deformation due to thick sediment in the northern Japan Trench is shown to generate efficient short‐wavelength seafloor uplift (>5 m), which is several times larger than the uplift by elastic dislocation models and generates impulsive tsunami that can have a large impact on the rugged Sanriku coast. Seismic moment due to inelastic wedge deformation has a reverse faulting focal mechanism with a steep plunge (>75°) of T axis, reflecting high efficiency in tsunami generation. However, the inelastic deformation is a large energy sink, which causes slower rupture velocity, weaker radiation of ocean acoustic and seismic waves, and ∼10 times lower moment‐scaled radiated energy than those of elastic models, explaining nearly all the anomalous characteristics of this tsunami earthquake. The anti‐plane off‐fault shear stress in the mode III rupture direction, limited by yielding, plays an important role in the slow rupture velocity and energy radiation along strike. Ocean acoustic waves may not provide robust signals for tsunami early warning due to weak high‐frequency radiation. Additionally, large, long‐duration ground velocity pulses can naturally result from inelastic deformation.