The thermodynamic modeling of underground coal gasification (UCG) is a very complex problem. We have just completed a survey of current status of UCG models. Models can be applied to the air bubble, initial linking, combustion link enhancement, or forward gasification phase. Chemical reactions can be treated as local, distributed, or overall phenomena. Heat transfer can include wall conduction, bulk gas convection in a cavity or porous zone, and radiation with an optically thick, translucent, or optically thin gas. Sloughing or swelling of the wall material as well as the influx of water may be treated in various ways. Most models employ several basic concepts or equations and utilize one or two dominant mechanisms to obtain a model which is tenable with computer memory and run time limitations. Models employing basic constitutive equations plus chemical reaction subroutines are therefore limited to the number of finite difference nodes which can be used and hence have geometry definition limitations, as well as process limitations. The Lawrence Livermore National Labs model, which is one of the better models available today, is limited to 2-Dimensions (thin seam only) and requires input data based on field test output data to obtain a reasonable match of cavity shape. Perhaps the most comprehensive effort under way is at ARCO, where it appears that a finite element program will include almost all aspects of the UCG problem and will require the use of a Cray or equivalent super computer which uses a CDC Cyber 76 or equivalent, as an input/output processor.