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The book is mainly concerned with the development of software utilizing explicit integration schemes to evaluate the integrals of rational functions of a n-th degree bivariate polynomial numerators with linear denominators over a 2-square in the local parametric space ( , ) to evaluate the element matrices for the Linear convex quadrilateral finite elements of lower to higher orders. Through application examples(specially torsion calculation )it is demonstrated that the available popular Finite Element Method (FEM) software requires sophisticated powerful computers and more computing time than the software presented in this book.On the other hand, the developed software is independent of the quality of computers, any computer can use it.Finally, user friendly software in FORTRAN based on the developed algorithm is presented in this book.Thus, I strongly believe that the developed software will be helpful for the post graduate students in Physics, Mathematics, Engineering and the researchers in Continuum Mechanics. Scientists and the Engineers who are interested in the analysis before designing and manufacturing may use this software as their analysis tools.