Abstract: 2-D radiation heat conduction equations have multi-scale characteristic and strong discontinuity.The asymptotic expansion method is  effective to solve such problems,whose main idea is to decompose the elliptic vector equation with multi-scale characteristic into several elliptic vector equation with smooth  (or single-scale characteristic) coefficients.For a kind of linear radiation heat conduction equations,this paper designs and analyzes a linear finite element method based on the asymptotic expansion，and gives corresponding error estimation.

Key words: 2-D radiation heat conduction equations；asymptotic expansion method, multi-scale characteristic, single-scale characteristic