Abstract: A general numerical model is given to identify parameters of the radiation boundary conditions for inverse hyperbolic heat conduction problems using Gauss-Newton method. The finite element is used for the discretization in the space system and a time stepping scheme is used for transient analysis. The inverse problem is formulated implicitly as an optimization problem with the cost functional of squared residues between calculated and measured quantities. Single and combined identifications can be carried out for thermal parameters and radiation boundary conditions etc. Satisfactory numerical validation is given including a preliminary investigation of effect of noise data on the results. Results show that the proposed numerical model can identify single and combined thermal parameters and radiation boundary conditions for hyperbolic heat conduction problems with precision.