The main results on non-classical problems of fracture mechanics obtained by the author of the monograph and his students over the past 50 years on the subject of the Department of Dynamics and Stability of Continuous Environments of the S.P. Timoshenko Institute of Mechanics of NAS of Ukraine are given briefly. Non-classical problems of fracture mechanics are defined as those in which the approaches and criteria of fracture of classical fracture mechanics are not applicable. These results have no analogues in the modern world scientific literature on the problems under discussion. For a wide range of specialists in fracture mechanics and related problems, in connection with which information on the mathematical aspects of research methods and their computer implementation is presented only in the form of a brief annotation.