The elastodynamic equations for the caustics formed from light rays reflected from the vicinity of the instantaneous position of the tip of a running crack were established for the case when the crack propagation velocity is considered as constant. For the study of elastodynamic stress intensity factors K'FI and lq, it is necessary to know the expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. The distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen, containing a transverse crack, running under constant velocity, was studied on the basis of complex-potential elasticity theory, and the influence of this form on the value of the dynamic stress intensity factors was given. The method was applied to the study of a propagating crack under mode I or mixed-mode deformation in a PMMA specimen under various propagation velocities, and the corresponding dynamic stress intensity factors Ig and Kil were evaluated. As an application, the method was used for studying the propagation of cracks under an initially mode I deformation in iron-epoxy particulate composite specimens under various filler-volume fractions and in different types of composite biphase specimens, as well as in specimens under prevailing plane-stress conditions containing different kinds of material discontinuities.