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The article deals with problematic issues related to the complex processing of materials that are heterogeneous and complex in composition and properties. The necessity of its technological modernization and development is substantiated on the basis of assessment of the technical level of the existing equipment. For the first time, the concept of creating technological machines with a kinematically deformable wave working chamber is proposed and substantiated. Variants of technological solutions for one- and two-wave apparatuses have been developed. They can be used for mixing, grinding and separating materials by size. The main features of the behavior of flexible wave surfaces when interacting with the processed medium are shown. The design of two experimental installations is described, their technical characteristics are given, the composition of the processed materials is stated. The results of experimental studies on the processing of quarry chalk, building mixtures and municipal solid waste are presented. The data obtained make it possible to judge a sufficiently high technological efficiency and the need for further development of devices with wave working equipment, which is expressed in a sufficiently high quality of the products obtained, the ability to control their particle size distribution, the ability to work in conditions of an abrupt change in the properties of the treated medium, including due to self-cleaning elements of the working chamber and the elimination of jamming of pieces of material in the working areas and the combination of various technological functions in one apparatus