The article deals with the problems arising from using the well-known analytical approaches to assessment of regional economic growth. Identifying the main factors of economic growth, study and analysis of the mechanisms of their influence on regional development can be considered one of the most pressing issues in modern economic research. This is because Russia has actually been in a state of «new normality», characterized by extremely sluggish economic dynamics and lack of clear prospects and models for bringing the economy out of this state, for the past few years. Obviously, it is not enough to search for new growth drivers; sect oral and territorial structure of the economy has to be modernized, with growth poles formed and prerequisites created for reducing the level of differentiation of regions according to basic socio-economic indicators. At the same time, the new approaches developed in the state policy of regulating socio-economic development should take into account the regional specifics engendered by a complex of objective and subjective reasons. The analytical form of dependences is chosen based on time and space series using statistical methods. Certain difficulties also arise in measuring GDP or GRP in comparable prices over a number of years. Analysis of existing methods and models described in the literature lead us to conclude that tools such as econometric models, systems of econometric equations, production functions should be primarily used. Comparing the main models of economic growth with empirical data has confirmed that it is necessary to adjust the existing approaches and develop new ones for assessing the dynamics of economic development. We have proposed a hybrid model based on production functions. Using the model in practice should allow to more adequately assess the structural and dynamic processes that accompany economic growth in the regions, as well as exert a more active influence on it by measures of state economic (regional) policy.