For the first time, a historical overview of the development of hypotheses and theories on the nature and mechanisms of destruction of brittle and plastic materials has been conducted. The contribution of Ukrainian experimental scientists and theorists, in particular B. E. Paton, G. S. Pysarenko, V. V. Panasyuk, and others, to the development of modern mechanics of deformed bodies is shown. The main causes of destruction of machine parts and elements of building structures are physical and chemical factors. In order to identify mechanical factors, the existing force fields of the structure are studied, the maximum stresses near the concentrators and the center of destruction are established, its macro- and microanalysis is performed, residual stresses and deformations are determined, and defects such as cracks, brittle zones, dislocations, etc. are found. To define chemical factors, the surface in the failure zone is analyzed, the nature of the chemical reaction at the end of the corrosion crack is determined, the causes of local changes in the material structure are diagnosed, etc. To eliminate or reduce the risk of failure, it is necessary to modify the design as required, replace the material, eliminate external causes, and perform additional technological operations, such as applying protective coatings. There are various theories of destruction. The presence of structural inclusions such as grains, microcracks, and dislocations in virtually all materials leads to their strength becoming significantly lower than theoretical. At the same time, the greater the defectiveness of the structural material (the deviation of its structure from the ideal), the lower the strength under other identical conditions. If destruction occurs under the action of repeated or cyclic loading, it is called fatigue destruction. This phenomenon was discovered by W. Rankine and A. Weller over 100 years ago. Today, fatigue mechanics is the basis for the design and calculation of most dynamically stressed structures and machines. This is due to increased operational reliability, reduced weight, and improved economic performance of structures. Thanks to the work of scientists from Ukraine and Western European countries, a variety of testing machines have been created in recent years, which have been put into practice in various countries (Germany, France, Belgium, Great Britain, etc.), based on the work of M. M. Davydenko, I. A. Odin, S. V. Serenesen, G. S. Pysarenko, E. O. Paton, V. I. Trufyakov, Ya. B. Friedman, O. M. Guz, V. I. Panasyuk, S. V. Malashenko, and others, appropriate modern testing machines, measuring instruments, and devices have been created, and relevant research has been conducted. This allowed the fundamental knowledge obtained about the mechanical properties of materials to take one of the leading places in world science. Domestic scientists studied the strength and creep characteristics of many materials depending on different deformation rates and temperatures, and established the presence of residual stresses and other factors. It should also be noted that in recent years, new methods of experimental research have come into practice, such as electro-tensometric, polarization-optical, membrane analogy, lacquer coatings, ultrasonic, X-ray, laser, and others. Further technical progress is impossible without the creation of new methods of experimental research of the mechanical properties of materials.