Aimed both at the researcher and the practicing engineer, as well as the student, the book is naturally divided into four parts. Part I (Chapters 1-3) introduces the fundamentals of modelling in a 1-dimensional framework. Part II (Chapter 4) presents the most important aspects of solidification theory related to modelling. Part III (Chapter 5) describes the fluid flow phenomena and in part IV (Chapter 6) the stress-strain analysis is addressed. For all parts, both numerical formulations as well as some important analytical solutions are presented.As a very deliberate choice, all the numerical formulations in the book are developed in the same framework based on the Finite Volume Method (FVM). This makes the differences and similarities between the formulations of solidification, fluid flow and stress-strain problems transparent and clear.