This paper studies the optimal tax authority resource allocation between two functions: the investigation and imposing penalty of the tax evasion. For this purpose the dynamic control model of the tax evasion environment is built. It has three phase coordinates: total amount of income for non-investigated tax evasion cases, amount for investigated ones for which penalty is not imposed yet and amount of funds returned into state budget as a result as a result of investigation and penalty of tax evasion. Based on theoretical plausible hypothesizes about tendency of tax­payers to the tax evasion and efficiency of tax authority's work the set of differen­tial equations is presented. 
The task for finding minimum of the total amount of non-investigated and not yet fined evasions is set and resolved on the basis of Pontryagin's Maximum Princi­ple. The question of the practical realization of solutions based on deterministic ap­proximation is considered.