FinFET transistors are playing an important role in modern technology that is rapidly growing. Embedded memories based on FinFET transistors lead to new defects that can require new embedded test and repair solution. To investigate FinFET-specific faults the existing models and detection techniques are not enough due to a special structure of FinFET transistors. This paper presents a new strategy for investigation of FinFET-specific faults. In addition to fault modeling, a new method is proposed for test algorithm synthesis. The proposed methodology is validated on several real FinFET-based embedded memory technologies. Moreover, new faults are identified that are specific only to FinFETs.