The paper addresses the methodology of research on the sustainable development of the Eurasian Economic Union (EAEU) financial market, the main elements of which include relevant concepts, hypotheses and approaches to testing these hypotheses. The paper describes the most important initiatives in the field of financial integration of the EAEU. The author's interpretation of the concepts of sustainable finance, joint priorities for sustainable financial development, and sustainable investment is presented. Research hypotheses are formulated regarding the choice of priorities and vectors of the EAEU financial market sustainable development. Methodological approaches to testing these hypotheses are proposed and approbated. The developed methodology allows to specify the directions for implementing the sustainable Finance paradigm in the strategy for forming the common financial market of the EAEU, with an emphasis on institutional conditions and new classes of financial assets in the context of national priorities for sustainable development and the specifics of financial systems. The reported study was funded by RFBR according to the research project № 19-010-00526.