Financial decisions that take into account long-term social, energy and environmental consequences should be determined as the the key point for the sustainable growth of the oil and gas industries in many countries all over the world, including Russia and China. The oil and gas industry transition to “Green Finance’’ in these two countries is represented by a new mathematical dynamic model, which uses the Ricci tensor analysis. For a sustainable growth analysis (a) Financial sustainable growth index (FSI), (b) Higgins’ sustainable growth rate (SGR Higgins), (c) Ivashkovskaya’ sustainable growth index (SGI Iv), (d) Varaya’ sustainable growth index modification (SGI modif) was analyzed and the graph’ average weights of the Ricci curvatures (Re) are compared. The links between financial sustainability and nonfinancial factors were found. Comparative analysis of the development of the China and Russia petroleum industries shows that China is developing more steadily. The R- values for each period are higher for China than for Russia. © 2021, International Journal for Quality Research. All rights reserved.