Modern enterprise exists in complex and dynamic environment. Non-stable finance-economic conditions, strict struggle for the consumer, change of the demand structure, the appearance of principally new modern goods and markets under such conditions of the life-length of the enterprise existence greatly depends on its ability to reach quickly competitive advantages and carry out changes in organization that is to depend on enterprise flexibility. Under modern conditions when enterprise is considered as a multinational market subject, the priority in investigation should be placed on organizational flexibility. From this point of view the topic of these researches is much attractive. Approaches to the determination of the notion "flexibility" are considered and also the classification of the signs and type of flexibility is generalized. The essence of the flexibility organization has been researched and the signs of its forming through the analysis of the known models of the organization such as: M.Weisbord’s "Six-Box" Model, McKinsey "7S" model, Berka–Litvin Model, and R.Daft Model. Further investigation may be directed on forming analytical tools considering organizational structure analyses, determination of its signs and selection of management criteria.