This paper introduces the algorithm of the risk assessment system in terms of sending messages in a social network (both within the personal correspondence of two users, and when publishing a message for an arbitrary number of users that are part of a community or a group). Such a system can be embedded in a common framework for identifying and blocking destructive content in social media. The work presents a model of interaction of actors when sending a message, and describes the approach to solving the problem of multi-criteria risk assessment of transferring the destructive content based, as well as forming the corresponding discrete value scales and specified convolution matrices. The use of such system allows efficient management of the resources of the social network hardware through a priori simplified procedure of content verification, while in-depth (or enhanced) verification of the contents (or its transmission to a moderator) is only carried out if the value of the integral risk coefficient exceeds the specified threshold. The proposed risk assessment system can be used both for real-time verification of messages sent, on request of the moderator, or on-demand (if there are complaints from the users). The paper contains the simulation results of the work of the proposed algorithm in the MATLAB environment for different numbers of recipients of the message, values of content destructiveness, and sender trust coefficients.