Main aspect of this thesis is the definition of approximation algorithms for the determination of state functions of water and steam. Before formulating and scrutinizing these algorithms, the first part provides the basic foundations of the field of thermodynamic state functions. Based on a common understanding of thermodynamics, important state functions, which are carried out by applying the first and the second law of thermodynamics, are used later on, in the approximations. Furthermore, the concept of fundamental thermodynamic relations is explained, especially considering the formulation IAPWS-IF97 published by the International Association for the Properties of Water and Steam (IAPWS). By using this industrial standard, the second part of the thesis deals with possible formulations for the approximation of the state functions of water and steam not only for the single-phase region, but also for the two-phase region. After defining these either linear or quadratic approximation functions the errors which occur when the respective characteristic parameters of each algorithm vary are investigated. Finally, a basic example for the use of the developed approaches is presented.