In modern mechanical engineering, vibrations play an extremely important role. Even with small variable loads, the lack of properly conducted analysis of vibrations or dynamic stability may lead to irreversible damage. The use of modern solutions such as the implementation of piezoceramic elements, appropriately selected damping, specially designed heads in loaded slender systems or heat treatment resulting in enhancement of internal structure of the material allows one to design modern and durable structures.Vibrations of molecules propagating in an elastic medium create mechanical waves. The analysis of this phenomenon in continuous media allows one to produce modern structures such as phononic crystals or metamaterials, which, thanks to their unique properties (the presence of a phononic band gap) leads to the design of devices that control the way energy is transferred in an elastic media. This creates the possibility of manufacturing devices such as acoustic diodes, waveguides, selective filters, mechanical wave mirrors, and many others.This Special Section of BPAST will be devoted mainly to the selected papers presented at the International Conference "Applications of Physics in Mechanical and Materials Engineering APMME 2021" organized online in 2021 by Częstochowa University of Technology. The conference was attended by over a hundred participants from research centers located in such countries as Bulgaria,