A numerical procedure, incorporated with the finite element solutions, is developed to evaluate the J(k)-integrals associated with crack kinking for a stationary crack in two-dimensional anisotropic elastic solids under dynamic loading conditions. In this paper, the formulation is shown analytically to be corresponding with the dynamic energy parameter and is clearly applied as a fracture criterion just before kinking takes place. The approach is verified to be path-independent in a modified sense. Special attention is also addressed to the simulation for the portions of integration around the near-tip region so that accurate solution is achieved without using any particular singular element. With the maximum energy release criterion, the predicted kink angle extracted from the transient numerical fields under steady loading condition is found to be inherently invariant, associated with each peak value of the energy parameter, and appears to be very close to that in the static case.