Under the economical-mathematical apparatus of multi-indicated estimation of the shadow economy dynamics in region quantitative estimation of factors made an impact on exchange of shadow economy volume was carried out. Modeling also has allowed to reveal the indicators adequately estimating dynamics of shadow economy. On the basis analysis of shadow economy of regions we worked out the conception for neutralization of shadow economy in UFD, based on optimum parity of economic and administrative measures.

Modern concepts of an estimation of interaction of the state and business are considered. The conclusion is drawn on perspectivity of development of the infrastructural approach. The basic threats to development of a market infrastructure of the Russian economy are revealed. Direction of neutralization of these threats are offered.

On the basis of a quantitative estimation of damage, inflicted by the shadow economy to region, draws a conclusion about priority of counteractions to schemes of evasion from the taxation. The criteria, allowing defining actions of the tax bearer as realization of schemes of evasion from the taxation, are formulated. The qualifier of such schemes is offered. Methodical approaches for revealing participants of schemes of evasion from the taxation are stated. They are based on formation of a characteristic structure of the tax bearer by means of application of the mathematical device of recognition of images and the analysis of results of interrogations of the businessmen spent on a case-technology.

A conclusion about assess method of shadow economy and decreasing its damage to the region economy. The methodology provides diagnostics of current and forecast crisis conditions caused by influences of shadow economy. The developed methodology is applied at consequences analysis of the actions against shadow economy damages bringing to social and economical development.

The importance of perfection tax administration for maintenance of financial safety is noted. The analysis of a current condition and prospects of tax administration in the Russian Federation is lead. Offers on perfection organizational and a supply with information of tax administration based on modern organizational and information technologies are formulated.

The influence of socio-economic consequences of world economic crisis on the regional shadow economy was studied in this article. As a result the economy-mathematical model of the regional shadow economy in the conditions of the world economic crisis was developed. The offered model was used for forecasting of a shadow activity dynamic under the influence of crisis tendencies in the economy.