The article presents implementation of modern methods for producing one-, two-, and three-dimensional composite matrices for tissue engineering based on resorbable and non-resorbable polymers. Coagulation method for producing composite fibers based on chitosan and chitin nanofibrils, electrospinning method for composite nanofibers, lyophilization of chitosan solutions and their mixtures with nanoparticles to obtain three-dimensional porous matrices with increased stability of mechanical characteristics in aqueous media have been described. The results of the studies in the adhesion and kinetics of proliferation of stem and somatic cells of humans and animals on the developed matrices were given. In vivo experiments showed that materials in the form of fibers, films, tubular samples, and sponges could be used as implants for blood vessels and effective wound dressings. Moreover, the article contains the findings of an investigation into the kinetics of resorption of the involved materials in a living organism.