The overarching goal of this study is to improve our understanding of the extinction characteristics of spherical diffusion flames in microgravity. In particular, one of the key objectives is to assess the effects of gas radiation as a means to promote flame extinction. To investigate these phenomena, a one-dimensional Computational model was developed to simulate the evolution of a spherical diffusion flame with consideration of detailed chemistry and transport properties. The model formulation was described along with the detailed numerical method. Radiation model was discussed with two aspects: radiation property model and radiative transfer model. Various levels of radiation models were implemented and the results were compared with experimental measurements of flame radius and temperature profiles. It was shown that the statistical narrow band model (SNB) combined with the discrete ordinate method (DOM) reproduced the experimental results with highest accuracy, and this combination of the radiation models were adopted in the subsequent parametric studies in Part II. Computational issues to optimize numerical accuracy and efficiency are also discussed. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.