The caustics method as applied to the measurement of the impact fracture toughness KId is studied by using a three-dimensional finite-element method (3D-FEM). A semi-infinite crack in an elastic plate with a finite thickness is considered, and a time-dependent (ramp) uniform pressure is assumed to be applied to the crack surfaces. The dynamic J-integral, J, is calculated for various points on the crack front and is converted to the dynamic stress intensity factor KI(t). The crack is assumed to begin to propagate when the value of KI(t) at the mid-thickness of the plate reaches a critical value Kcrit. The caustics in reflection are generated by using the reflection law of light. The "measured" KI(t) is obtained from the diameter of the caustics, and the "measured" KId is determined from the peak of the time history of the "measured" KI(t). It is found that the delay time to detect the crack initiation is larger than that predicted by 2D-FEM, and the "measured" KId depends on the shape of a propagating crack front.