The problem of evaluation of effectiveness of advertising has not yet been solved. The effectiveness of advertising depends on two factors: the creative concept of advertising message and optimization of placement of advertisements. Quite often the role of the second of these factors is underestimated. In this regard, the development of analytic theory of media planning is very important. The most thoroughly investigated questions are the questions of efficiency of influence of advertising messages on the audience. In this paper an economic-mathematical theory of media planning is developed. Within the framework of this theory the analysis of spectrum of reach of the audience is performed; the methods of calculation of effective multi-media reach of the audience are developed; the concept of risk of advertising in the media is defined and technique for its calculation is provided; the problem of optimization of placement of advertisements is solved. The methods of risk calculation of advertisement placement in the media are developed; the concepts of effective and optimal number of advertisements to be placed in the media are introduced; the dependences of effective number of advertisement placements on the magnitude of risk and on the magnitude of effective frequency are calculated.