In respect of the fact that a rigid body may consist of infinitely many particles to form a continuum, the specifications and the balance equations of a continuum are discussed first in this chapter. The constraint of a rigid body is then specified such that the dimension of the body is reduced significantly from infinity to six, including three for translation and three for rotation. Instead of the Euclidean spaceEuclidean space for the translations, the set of rotation dyadics is used to describe the rotational motion. After the concept of moment of inertia is introduced, the equations of motion for a rigid body are established, which contains Newton’s equation for translation and Euler’s equation for rotation. Various parametrizations such as Eulerian angles and the unit quaterions are introduced to represent the rotations. For rigid bodies in contact, Coulomb’s law of friction and the law of collision are discussed which may be required to determine the motion.