The Second Generation Model (SGM) is a computable general equilibrium model designed specifically to analyze issues related to energy, economy, and greenhouse gas emissions. It has fourteen global regions, multiple greenhouse gas emissions, vintaged capital stocks, explicit connections between technology and the economy, explicit treatment of energy and land stocks and is disaggregated to reflect the relative importance of sectors in determining greenhouse gas emissions. Model development began in 1991. The first model design paper was published in1993 (Edmonds, et al., 1993). The SGM was developed to complement the first generation model, referred to as the MiniCAM. The MiniCAM was alsoexplicitly designed to address long-term, strategic issues related to energy, economy, and greenhouse gas emissions (Edmonds and Reilly, 1983)and continues to be used for that purpose. In contrast the SGM was designed to address transitional energy-economy- technology-greenhouse- gas-emissions issues. This paper documents the present version of the SGM: SGM 2004. The SGM 2004 consists of a theoretical structure, computational implementation, and statistical expression. This paper documents the theoretical structure and some of the most important data shaping model behavior. It does not attempt to document the software employed to solve the statistical expression of the theoretical relationships nor does it provide a complete documentation of all of the data employed in SGM 2004. The SGM was developed at the Pacific Northwest National Laboratory (PNNL) and ismaintained by the PNNL Joint Global Change Research Institute (JGCRI).