Abstract: Based on numerical calculation and error distribution mechanism of the linear entity in vector GIS,the modeling error theory of 2D generic curve in vector GIS has been researched.The concept named the equivalent probability density error model(Tepdem) is brought forward.The concepts and ascertaining methods on Scale factor used to determine the scale of Tepdem are presented.Based on the probability algorithm on a linear entity drops in its corresponding Tepdem and the probability confidence level,the scale of Tepdem to 2D generic curve are solved successfully.The theory and methods are provided,at the same time,the theory basis for GIS positional uncertainty research has been tamped to great extent.