Unlike modern maps, geometric maps lack a coordinate system and contain unsystematic geometric inaccuracies. This paper illuminates four aspects concerning the problem of uniting geographical information technology with old geometric maps. These are as follows: first, the origin of and geometric qualities in the representation of objects in geometric maps; second, the distortions originating from measurement techniques; third, the assumption that it is possible to find points that are the same over time for rectification in Geographic Information System (GIS); and, fourth, the extrapolation of unsystematic geometric distortions when using GIS techniques without any knowledge of the present unsystematic distortions in a map. The article presents the background of Swedish geometric maps and a hypothetical example is used to present the principle problems of using GIS techniques to rectify geometric maps. The conclusion of the paper is that systematic and unsystematic geometric distortions need to be identified and handled separately.