We consider a multidimensional model of opinion dynamics in social networks. Within the framework of the model, the dynamics of two interconnected information processes in a social network is studied. The first process is the process of spreading of the excitation in the network of agents and their actions observed from outside (e.g., in the form of messages posted in social media). The second process, which has a connection with the first, is the formation of agents’ opinions (which are a characteristic of their internal state). We demonstrate that the proposed model of opinion dynamics is flexible and allows taking into account the significant effects of opinion formation in social networks, including consensus or agreement of opinions, preservation of differences in agents’ opinions, and even polarization of opinions. We propose approaches to measuring the polarization of opinions and present simulation results. We show that the proposed polarization index for a network allows one to distinguish and evaluate situations with meaningfully different multidimensional distributions of opinions in a social network as well as to find directions of the greatest polarization.