The Proceedings contain theses of papers presented at the Fourth International Conference “Modern Problems in Modeling Materials for Mechanical, Medical and Biological Applications” (MPMM&A-2024). The conference focused on the results of work in the following areas: contact problems of elasticity theory for media with complex mechanical properties; modelling of hard and soft biological tissues; modelling of composite materials; modelling of piezoactive materials; actual problems of computer engineering; training of modern engineering personnel. Fourth International Conference “Modern Problems in Modeling Materials for Mechanical, Medical and Biological Applications” (MPMM&A-2024) (November 18-22, 2024, Rostov-on-Don) was supported by a grant from the Russian Science Foundation No. 22-19-00732.