This paper describes a newly developed statistical approach for modelling positional error of geometric features in GIS. The generic statistical models for N-dimensional features are firstly derived. The models for one- and twodimensional features are then developed as the specific cases of the generic models. In each dimension, the GIS features are classified as points, line segments and line features. Because of the errors, features stored in GIS may not correspond with their actual location in the real world. The true location of a GIS feature is only known within a certain area around the represented location in GIS. This newly developed approach can be used to provide a statistical description of such areas. For one-, two- and N-dimensional GIS features, they are defined as confidence intervals, confidence regions and confidence spaces respectively. The areas are related to the positional errors of the composite points of the features and to the predefined confidence level. The models are derived based on the assumptions that the errors of the composite points are independent and follow multi-dimensional normal distributions.