This paper presents a new method to analyze the bidding strategies of Generating Companies (GENCOs) with regard to demand elasticity. It is assumed that the available information of each GENCO about its opponents is incomplete and only the minimum and maximum generation levels of their opponents, as well as their fuel type, are known. In the proposed methodology, GENCOs prepare their strategic bids according to a Supply Function Equilibrium (SFE) model. GENCOs will change their bidding strategies until Nash equilibrium points are obtained. The general Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with non Linear Programming (NLP).