Alloy design by the traditional trial and error approach is known to be a time consuming and a highly cost procedure, especially for the design of heat resistant steel where the feedback time is intrinsically long. The significant developments in computational simulation techniques in the last decades have made a theory-guided computational alloy design possible. Such a computational approach can substantially decrease the development time costs. In this thesis a computational alloy design approach coupling thermodynamics, kinetics and a genetic algorithm has been developed to design the non-corroding ferritic, martensitic and austenitic heat resistant steels for use at a high service temperature. In the design of heat resistant steels, the evolution of the microstructure and hence properties, depends on service time and temperature and should be considered carefully. For heat resistant steels deriving part of their high strength on precipitates the coarsening of the precipitates at high temperature is considered as the most important factor and this process features highly in the design. Novel steel compositions (involving typically 9 alloying elements) and associated key heat treatment parameters are considered and optimised. The calculated optimal compositions are unlikely to be perfect and free of experimental problems but form an excellent start to initiate experimental development programs and to substantially shorten the development time of new high performance steel grades.