The motions of particles and rigid bodies have been discussed extensively in the preceding chapters. While Euler’s laws of linear momentum and angular momentum, as described in Sect.  3.3 , can be directly applied to study the motion of a deformable body, extending variational principles can be useful for dealing with constrained problems, whether internal or external. In this chapter, the Principle of Virtual Power and the Hamilton Principle, described in Chaps.  5 and 7 , respectively, are extended to derive governing equations for a deformable body. This extension can be somewhat understood through the limiting process from the vibration of a series of beads to that of a continuous string. For the Principle of Virtual Power, the internal properties of the body are considered by including the internal energy function and the Rayleigh dissipation function. Cauchy’s first and second laws, as well as the constitutive relations, can then be established simultaneously. For the extension of Hamilton’s Principle, the strain energy is used to represent the internal structure of the body. An engineering model, the Euler–Bernoulli beam, is considered to illustrate the use of the extended Hamilton’s Principle and the corresponding variational process.