Abstract: A stochastic model of DEM linear interpolation is derived based on the stochastic process model,as well as an uncertainty description of its basic element——the irregular random spatial triangle.Error propagation of the TIN points in the linear interpolation is discussed.Through theoretical deduction and practical examples,we obtained the point-seat variance of the TIN DEM linear interpolation points,analytical expressions for three semi-axises of the error ellipsoid and the coordinate of the point in the DEM linear interpolation with the highest precision.The results has nothing to do with the shape of the triangle.Moreover,theoretical proof makes on the inevitability of the dramatically decrease of the precision caused by the DEM linear extrapolation.An analytical expression of the average point-seat variance of the TIN DEM linear interpolation is obtained.This model could uniformly describe the uncertainty of the points on the triangle and its sides.Through theoretical deduction and numerical test,we obtained the coordinate of the point in the DEM linear interpolation with the highest precision.