This book is the first volume of the trilogy Analytical models of thermal stresses in composite materials I, II, III , presenting, in each of the volumes, genuine results only created by the author. The fact that the author proceeds from fundamental equations of Mechanics of Solid Continuum confirms the genuineness of the results and accordingly establishment of new scientific school with an interdisciplinary character belonging to the scientific branch Applied Mechanics. As an imagination considered for the analytical models, an elastic solid continuum is represented by a multi-particle-(envelope)-matrix system consisting of components represented by spherical particles periodically distributed in an infinite matrix, without or with a spherical envelope on the surface of each of the spherical particles. The multi-particle-(envelope)-matrix system with different distribution of the spherical particles is considered as a model system for a determination of the thermal stresses in real composite materials with finite dimensions included in the categories.