This book is a treatise on the design of robust and accurate elements for applications in structural mechanics. It describes the epistemological conflict between the principles in finite element technology that can be described as Art and those that have a scientific basis. The main emphasis of the book establishes the process by which continuum structural behavior is replaced by a discretized description so that this can be coded as mechanics algorithms. Early efforts to do this were founded on engineering principles proceeding mostly from heuristic judgement (Art). However, considerable critical and analytical study in recent years has shown that it is possible to establish these methods on a more scientific basis. This book therefore sets this aspect of the use of the finite element method against such principles. It is an up-to-date account of the state-of-the-art of the theory of finite element development and its critical assessment.