Following the advance in computer technology, the numerical technique has made significant progress in the past decades. Among the major techniques available for numerically analyzing continuum mechanics problems,finite d- ference method is most early developed. It is difficult to deal with cont- uum mechanics problems showing complex curvilinear geometries by using this method. The other method that can consistently discretize continuum mechanics problems showing arbitrarily complex geometries isfinite element method. In addition, boundary element method is also a useful numerical method. In the past decade, the differential quadrature and generic differential quadratures based discrete element analys is methods have been developed and usedto solve various continuum mechanics problems. These methods have the same advantage asfinite element method of consistently discretizing cont- uum mechanics problems having arbitrarily complex geometries. This book includes my research results obtained in developing the related novel discrete element analysis methods using both of the extended differential quadrature based spacial and temporal elements. It is attempted to introduce the dev- oped numerical techniques as applied to the solution of various continuum mechanics problems, systematically.