This book - the authors' second book on screw compressors presents the results of the most up to date methods of three-dimensional modeling of the fluid dymanics and the solid-fluid interaction within these machines, which are still being developed. By including them in the design process, it is possible, not only to predict flow patterns more accurately, and hence improve the design of the critical components, but also to determine how the pressure and temperature distribution within the compressor distorts the rotors and casing and how this, in turn, has an interactive effect on the performance. Such calculating facilities are especially valuable for oil free machines, in which temperature changes are much larger and thus make thermal distortion effects more significant. However, it confers advantages in all cases, as improved machine tools enable manufacturing tolerances to be reduced and hence compressors can be built with smaller clearances. Four examples outline the scope of the applied mathematical model for three dimensional calculation of fluid flow and stresses in the solid parts of the screw machine.