Abstract: Firstly,we propose a new model namedεE model to measure line segments positional uncertainty,which consider the semi long-axis of the error ellipse at any point on the line segment as the width of the error band,that is,the positional uncertainty of line segment is considered as a set of error circles with the radius of the error ellipse's semi long-axis at any point on the line.Secondly,the analytic expressions of the error band boundary line for the εE model of line segment are deduced,the parameter equations of the error band boundary are gotten.Thirdly,three indexes are given to measure the precision of the line uncertainty based on the εE model: the visualization graph,the average error band width and the error band area.At last,the εE model is compared with the εE model and the εE model.Theory and practice show that εE model is simple in calculation but too limited in the error band width,εE model is scientific in theory but complex in calculation,and model is scientific in theory and convenient in practice though over-width in the error band width.