The dynamic stress field near the tip of a crack tip which is accelerated and decelerated in an elastic plate with finite width under impact loading is analyzed by the boundary element method, and a simulation of measuring fast crack propagation toughness KID by the caustic method is performed. The results of the simulation agree qualitatively with the experimental results by Arakawa and Takahashi, and indicate the dependence of the 'measured' KID not only on crack acceleration but also plate width. The dependence of 'measured' Km on crack acceleration may result from the fact that under the condition of high loading rate or abrupt change in crack velocity, the transient stress field near the initial curve of caustic can not be represented fully by the dynamic stress intensity factor Ki(t, v), as suggested by Rosakis et al. The dependence of 'measured' KID on plate width may be attributable to the fact that the transient stress field near the initial curve is affected directly by the reflected stess wave and also indirectly through crack acceleration which depends on the reflected stress wave. The possible dependence of the 'measured' KID on loading rate, loading history, crack propagation history is also discussed.