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The elastodynamic response of the transformation-toughened ceramics under an instantaneous phase transformation is investigated. Some composite materials, such as Zirconia toughened ceramics, are the remarkable material, which has a high strength, a high elastic modulus, and an improved toughness, etc. Most of the good qualities are common in many ceramic composite materials. These good qualities are made possible through the phase transformation of composite particles. The transformation toughening utilizes the stress-induced phase transformation of particles, which is accompanied by a volumetric expansion. In this paper a phenomenological model is proposed to describe the situation, which involves a dynamic martensitic transformation in a spherical particle of Zirconia embedded in an infinite elastic matrix. Following the ray methods, we clarify the stress-focusing effect caused by the instantaneous phase transformation in a spherical inclusion of Zirconia. It should be noted that the mechanism in the toughening of ceramics in the steady state does not hold in the dynamic state.