The main objective of this Ph.D. thesis is to describe and analyse the most recent knowledge about operational flexibility in steam power plant evaporators, based on mathematical / numerical methods. The thesis addresses a mathematical study of steam power plant evaporators and involves the reader in many of the complex considerations-, that are necessary to initiate such a study of thermal-hydraulic two-phase flows. The model complexity is increased with the transport of a fluid that changes phase from a sub-cooled liquid state, to a superheated vapour through the evaporator. The mathematical models include analysis of static stability, in the form of studies of mal-distribution in panel walls and Ledinegg stability. Additionally dynamic studies of start-up conditions and load control examples are performed. The choice of the numerical scheme has focused on a higher-order scheme, which can handle steep gradients, discontinuities and shock in the solution and can handle dynamic effects through boundary conditions and initial fields. Furthermore, the thermodynamic properties associated with the flowing media are modelled as a fast look-up table, which in this case is water/steam. The reader will be introduced to basic concepts in the power sector, including lifetime terms, such as corrosion, creep and fatigue, related to the evaporator tubes, which are responsible for the transfer of energy from the boiler to the water / steam circuit of a power plant. New evaporator technologies are briefly described, followed by a simulation of a steam power plant evaporator of Skærbækværket (SKV3), which is one of DONG Energy’s ten central CHP plants, built in 1998 and located in Skærbæk at the mouth of Kolding Fjord in Denmark. Here different heating profiles of the evaporator are investigated, as well as an examination of the consequences of a feed water preheater outfall and reduced evaporator pressure, which are some among many other actions that can be analysed to adjust the thermal power stations to the new market conditions requiring increased green energy. The numeric scheme is particularly well suited to handle strong oscillations and slugs in relation to the two-phase flow, and in spite of the associated water / steam library being designed as a fast bilinear ’look-up’ table, the calculation time is long. The structure of the application is generic in the sense that other fluids can be used. The simulation tools are implemented in C++ and can communicate with various commercial tools, for the purpose of post processing of the calculation results.