This book is intended for senior and junior researchers and Postgraduate students who are interested in learning some fundamental aspects of non-Newtonian fluid mechanics. The people in the field of Mathematics, Chemical Engineering, Civil Engineering, Mechanical Engineering, Polymer Industries, and many other branches of Physical Sciences will get benefitted from the content of this book. It covers fluid mechanics and similarity solutions together. So readers can find both in one book. Also, it will offer many non-Newtonian models for readers. Present work is to demonstrate a couple of more extensions of the existing method for non-Newtonian flow problems. The equations derived in this book can be found in most engineering problems. Thus present extension with necessary modification of existing techniques adds more application of these techniques which are useful for the treatment of engineering boundary value problems. The present work is to demonstrate a couple of more extensions of the existing method for non-Newtonian flow problems. The equations derived in this book can be found in most engineering problems.