The model of formation of pipe-like kimberlite and lamproite bodies, which is based on the fluid dynamic regime of development of magmatic paleosystems, is developed. The main factors determining the fluid dynamic regime of formation of kimberlite bodies are formulated. The proposed model satisfactorily explains many morphological features of kimberlite systems represented by dykes, pipes and sills, peculiarities of the internal structure of kimberlite bodies composing them and may serve as the basis for developing criteria of their diamond potential.