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[en] A Runge–Kutta ray-tracing method for determining the thermal emissions of a two-dimensional semitransparent graded-index medium has been developed for this study. A backward ray-tracing method and a backward Monte Carlo method were employed in the calculations. The emission characteristics of a linear refractive index medium were investigated. The results of the Runge–Kutta ray-tracing method were shown to agree well with previously obtained exact solutions. The apparent emissivities of a radial refractive index medium obtained using the Runge–Kutta ray-tracing method fit the analytical solutions well. However, for a sinusoidally distributed nonlinear refractive index medium, the Runge–Kutta ray-tracing method revised emissivity results differed from the results of a linear refractive index bar model at certain angles. The results show that the Runge–Kutta ray-tracing method is effective in dealing with the radiative transfer problems of multidimensional graded index media. - Highlights: • Thermal emission of a two dimensional GRIN medium was studied. • Results by Runge–Kutta ray tracing method can regard as benchmark. • The method is simple and flexible.