The article discusses the mathematical modeling of the evolution and accumulation of scientific and applied knowledge; solving these problems is established as urgent for modern high-tech companies, the existing mathematical foundations are described, and the authors’ own proposals are presented. The problem of mathematically modeling knowledge growth is examined by the authors on two levels, which are the growth and evolution of general knowledge, and the accumulation of individual knowledge (knowledge of a particular individual). The growth of general knowledge is described by the law of exponential growth, which is consistent with the results of the previous studies of this phenomenon. Based on the formal representation of the process the authors have determined the parameters characterizing the evolution of knowledge in a particular subject area; these are the intensity of knowledge obsolescence and the knowledge half-life period. The article contains calculations of indicators for various fields of knowledge, shows their practical application in knowledge management systems of companies. The process of individual knowledge growth and accumulation is logically represented by a function of logistic dynamics. Logistic curve dynamics highlights the main stages by which employees accumulate professional knowledge in high-tech companies. Based on this, the authors describe a mechanism for determining the amount of knowledge corresponding to these stages and show the possibility of using these characteristics in the actual knowledge management in modern companies. The combination of the two processes (growth of general and individual knowledge) is described by an analytical formula that can predict the general level of knowledge in a company in the context of the development of the knowledge used in a particular industry. This, in its turn, determines the possibility of planning strategies and knowledge management activities within a company. The article presents the prospects for the further development and investigation of the evolution of the knowledge problem and its models, aimed, in general, at forming a full-fledged complex of knowledge management tools in high-tech companies.