For doctoral and postgraduate students majoring in Mechanical Engineering, based on Advanced Mathematics, Material Mechanics and other courses, this course mainly includes the basic concepts and equations of Elasticity, including the state analysis of stress and strain, rectangular and polar coordinate solutions for plane problems, solutions to the problem of cylinder under torsion. The purpose of this course is to enable students to understand and master the basic principles and methods of Elasticity to solve related mechanical problems in science and engineering, and to improve the basic mechanical literacy of students in this major.