World experience of rural development proclaims the following directions for regional stimulation: state initiative, unauthorized seizure, development of existing territories, cottage landscaping, etc. The purpose of the study is to identify perspective means for overcoming asymmetries and disparities in the development of territorial communities. The objectives of the study are: 1) Identifying existing asymmetries and disparities in the development of territorial communities; 2) Justifying socioeconomic instruments for achieving the goals of rural development. The research methodology is based on the results of field research conducted by the authors in the rural territories of Ukraine, as well as the experience of rural territories development in the Republic of Lithuania. The study is based on holistic and system-synergetic approaches. National policy's focus on urban development, as a source of budget revenue formation and economic growth, and little attention to rural development have contributed to the emergence of asymmetries and disparities at the regional level. The operation of modern Ukrainian communities is accompanied by problems of rural development, which contributes to the emergence of several structures that contribute to their resolution. The main reasons for people's migration to live in rural areas in Ukraine are retirement age, personal socioeconomic problems, personal beliefs about ecology. The research proves the existence of three basic approaches to defining a community – geographical (understanding the community as a territory), social (community as a set of different relationships), systemic (community as a definition of identity). Activation of communities depends on its leaders, the activities of change agents and the use of modern methods of encouraging their residents to work together and achieve their goals. The community can be involved in ensuring local development through the use of various methods and approaches. In particular, one of the effective methods is creating cooperatives. They have advantages over other forms of organization, first and foremost in a possible grouping of resources needed and flexibility in responding to changes in the environment. The creation of rural communities in Lithuania was initially aimed at solving social problems. Henceforth, they were able to solve economic problems. The results of the comparative evaluation of Lithuanian and Ukrainian rural communities' development are presented. One of the defining directions of ensuring rural socioeconomic development of Ukraine and other countries is forming a new worldview for people. It focuses on ecology, human unity with nature and the enhancement of natural resources potential, as one of the effective mechanisms that can ensure the development of a society. The article will cover the economic and mathematical model of socio-economic processes using the idea «Family homestead».