This chapter concerns the classical impact theory, although it starts with the Hertz theory of the impact of elastic spheres. We discuss in detail the concept of the restitution coefficient. We give a new deduction of the algebraic system of first and second kind Lagrange equations, corresponding to the classical impact theory of mechanical systems with ideal constraints. It is essential that this system of equations takes a particularly simple form in a number of tasks due to the use of quasivelocities. We consider the impact on a straight chain of rods and on a chain situated on a circular arc. The use of methods of solving finite-difference equations allowed us to build an analytical solution of the two given problems. We also consider other important examples.