This paper describes the technical challenges tied to modeling and design optimization of the medium frequency transformer (MFT) for power electronic applications, namely emerging solid state transformers (SSTs). A detailed analysis and modelling of the phenomena governing the MFT electrical behaviour as well as limiting the operation and design range is performed. A synthesis of all these models is done in form of a design optimization algorithm capable of generating the set of all feasible transformer designs. Moreover, design filters are developed allowing to search for the most preferable design alternatives in terms of hot-spot temperatures, weight, volume and efficiency. Finally, a full scale MFT prototype has been realized according to the optimal specifications outputted by the proposed design optimization tool.