The three-dimensional unstable non-linear coupled mathematical model on the underground coal gasification with free channel is established in this article. The determination methods for the major model parameters are explained. Adopting the SIMPLE method, the numerical solution of the mathematical model is found. Additionally, the patterns of variation and development for the temperature field, concentration field and pressure field in the gasification panel are studied. On the basis of the model test, the calculation results are analyzed. Research shows that calculated values of the temperature field are a little higher than the experimental ones, and the relative error for every measuring point is virtually within 16%. Also, a good conformity takes on between the experimental values for the concentration field of the gas compositions and the calculated ones. The simulated results indicate that the relative calculation error of the pressure field is 10.20%-19.44%. Through the analysis of measured data, the change mechanisms of the gas compositions, heating value and pressure field in the underground gasification with free channel are pointed out.