The continuum mechanics is based on the following theories: (i) geometric field theory describing the strains; (ii) laws of conservation of mass, linear momentum, angular momentum, energy; (iii) constitutive relations between strains or stresses; (iv) equation of state. Each of these theories may be linear or nonlinear, and global or local. The nonlinearity and global characters in the geometric field theory cause the rotations which in turn cause the asymmetry in the stress components. The presence of microstructures in the body or the external electric or magnetic fields creating the electric or magnetic poles in the body are also some of the causes which introduce asymmetry in the stress components. In the present article, the continuum medium is taken to be elastic and it has nonlocal and asymmetric characters, besides the nonlinearity. All relevant equations describing all these aspects are summarized. The theory is illustrated by taking a simple problem of one-dimensional plane elastic waves. The special features of such waves are indicated in detail supplemented by experimental data and graphs. The paper will be very useful to those who wish to start research in this area of continuum mechanics. The mode of exposition is also nice. However, a fair knowledge of the tensor theory is required to read this papers.