The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub-vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub-vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub-vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.