Several experimental studies have demonstrated that confined laminar diffusion flames established in an inverted burner are very stable and emit soot when the global equivalence ratio exceeds a critical value. An inverted diffusion flame can be used as a stable source of soot particles for development and intercomparison of various particle sizing techniques. Unlike normal coflow diffusion flames fired upward, inverted diffusion flames fired downward experience a negative gravity, the resultant flow fields are very different, and the residence time is significantly prolonged. The different flow fields in normal and inverted diffusion flames mean that the flame structure and soot formation characteristics are significantly different. This study makes a first attempt to numerically investigate the flame properties and soot formation in confined laminar coflow CH4/air diffusion flames established in an inverted axisymmetric burner at atmospheric pressure. A fairly detailed reaction mechanism, GRI Mech 3.0, was used to model combustion chemistry. Soot formation was modeled using a semi-empirical, acetylene-based, two-equation soot model. Radiation heat transfer was calculated using the discrete-ordinates method and a wide-band non-gray gas model. Numerical calculations were conducted over a relatively narrow range of global equivalence ratio of 0.54-0.67 based on a recent experimental study. The heat transfer boundary condition was found to be important to the prediction of soot emission and the velocity distribution. Using measured temperature distribution along the quartz tube, the numerical model successfully predicted the emission of soot under the conditions investigated and revealed the flow, temperature, and species concentration distributions in the inverted coflow diffusion flames for the first time. However, the predicted primary soot particle diameters are significantly smaller than those reported in the literature based on TEM images analysis of sampled soot. The discrepancies between the numerical results and experimental data can be attributed to the deficiency of the simple soot model and the approximate treatment of the heat transfer boundary conditions at the quartz tube.