This paper presents a model for describing the positional error of line segments in geographical information systems (GIS). The model is based on stochastic process theory with the assumptions that the errors of the endpoints of a line segment follow two-dimensional normal distributions. The distribution and density functions of the line segments are derived statistically. The uncertainty information matrix of line segments is derived to indicate the error of an arbitrary point on the line segment. This model covers the cases where two-end points are correlated to each other and points on the line segment are stochastically continuous to each other. The model is a more generic error band model than those previously developed and is called the G-Band model.