Participants in the restructured power market are seeking effective generation resource bidding strategies. This paper proposes a methodology to obtain the optimal bidding strategy for generation companies (GENCOs) participating in electric power markets. Supply function like model, which chooses to strategically bid generation prices of bid curves, is used here for the day-ahead market auction. Different strategies are used on different supply curve segments, and the inter-temporal physical constraints of units are considered to derive a multiple-period bidding strategy. Imperfect competition in realistic power markets is modeled as a non-cooperative game, with each participant holding incomplete information about its opponents. A two-layer optimization problem is modeled, with the upper layer representing the GENCO's profit maximization problem and the lower layer representing the independent system operator's (ISO) market clearing problem based on transmission constrained market clearing. Illustrative examples show the effectiveness of multi-segment, multi-period bidding strategies.