This book presents these recent advances in a simple way. The authors have been mainly concerned with producing a text for teaching which can be easily followed by the self-taught student. The last part will undoubtedly also be of use to research workers. The reader will be led from the basic principles of Chapter 1, and the simple finite element concepts and models given in Chapters 2 and 3, step by step to more complex applications. A chapter (4) on the governing equations of fluid flow has been included o provide a more complete progression, though this is not intended for those already well versed in fluid dynamics. Chapter 5 is concerned with the solution of potential type problems and Chapter 6 sets out viscous flow problems in porous media: both are topics well suited to finite element solutions and of general interest to the engineer, applied mathematician and physicist. Until recently, finite element techniques were almost exclusively used in structural engineering problems but now there is a growing awareness of their potential in other engineering fields, especially in fluid mechanics.