The dissertation is the first qualifying scientific work in Ukraine, after the entry into force the CPC of Ukraine from 2012, in which, on the basis of a complex analysis of problems of normative, legal and law enforcement nature, the concept of material evidences in the criminal process was developed and substantiated, taking into account the European legal standards of fair justice and ensuring the rights of participants of criminal proceedings. On the basis of the scientists works' analysis the process of formation of the doctrine of material evidences was described, the expediency of its isolation as an independent criminal procedural doctrine was grounded, the concept of the doctrine of material evidences was defined and its object, subject, purpose, tasks, meaning, system and methodological basis were disclosed in the dissertation. On the basis of the complex approach, the essence of material evidences as a legal phenomenon is disclosed by defining both their essential elements and the features, inherent to them. To the essential elements of material evidences it is proposed to attribute their contents and procedural form. The system of signs of material evidences, to which subjectivity, objectivity, informality and procedural certainty are included, has been improved. The author’s definition of the concept of material evidences is given and the author’s concept of material evidences in the criminal process is proposed. The system of procedural properties of material evidences is disclosed, their characteristics are described, and, taking into account the obtained results, the concept of belonging, admissibility and reliability of material evidences is determined. The criteria for classifying material evidences, the use of which will provide a comprehensive reflection of various aspects of this legal phenomenon and will allow taking into account the peculiarities of each type of material evidences in the process of their formation and use, are singled out. The further development of scientific provisions concerning the structure of criminal procedural proof in winch it has been proposed to allocate two elements (stages): the fonnation of evidences and use of evidences. The contents of the formation of material evidences during the pre-trial investigation was characterized and the peculiarities of the fonnation of material evidences during the judicial proceedings were detennined. The substantiation of the verification of material evidences by the defense side, the victim and the representative of the legal entity, in respect of winch the proceedings are being conducted. The doctrinal model of the depositing of material evidences in the criminal process is proposed. The legal model of the depositing of material evidences as a new sub-institution of criminal procedural law is substantiated. The place of use of material evidences in the structure of criminal procedural proof is found out. The ways of use of material evidences to the number of which it is proposed to attribute their use by the investigator, prosecutor, investigating judge, court for substantiation of procedural decisions, their use for verification of available and obtaining of new evidences, their use by the sides of criminal proceedings for substantiating of their legal positions are generalized. The concept, essence and contents of material evidences' storage as a condition of ensuring the inviolability of property rights are disclosed and the terms, procedure and conditions of their storage are characterized. The doctrinal definition of the contents of the material evidences' storage lias been improved. A mechanism for the transfer of material evidences to storage (responsible storage) has been developed. The moment of the beginning and the moment of the expiration of the period of storage of material evidences are detennined. The ways of the issue solution concerning the fate of material evidences during pre-trial investigation and judicial proceedings are characterized and the order of solution of their fate by the investigating judge and the court are described. The condition of the ways of solution the material evidences' fate by their types is proved. The necessity of ensuring the priority of the material evidences' return as a way of their fate solution was justified. The theoretical positions, concerning the necessity of improving the normative consolidation of the grounds for compensation of damage, caused by loss or damage of material evidences, have been further developed. Based on ECHR practice, the European legal standards for compensation of damage, caused by loss and damage of material evidences, are singled out. Based on international legal acts and ECHR practice, the European legal standards of the formation and use of material evidences in the course of criminal proceedings and the provision of property rights to material objects, seized as material evidences in the course of criminal proceedings, have been characterized. The scientifically substantiated proposals, aimed at improving the CPC of Ukraine in the field of the concept of material evidences, their formation, use, storage and solution of the issue about them during criminal proceedings, have been developed.