Nowadays, location-based data collected by GPS-equipped devices such as smartphones and cars are often stored as spatio-temporal sequences of points denoted as trajectories. The analysis of the large generated trajectory databases such as the detection of patterns, outliers, and stops has a great importance for many application domains. Over the past few years, several successful trajectory data infrastructures have been progressively developed for a large range of applications in both the terrestrial and maritime environments. However, it still appears that amongst many research issues to consider, the resulting uncertainties when analyzing local trajectory properties have not been completely taken into account. In particular, determining for instance certainty rates, while detecting stop points, might have valuable impacts on most cases. The framework developed in this paper introduces an approach based on the Dempster-Shafer theory of evidence, and whose objective is to detect trajectory stop points and associated degrees of uncertainty. The approach is experimented using a large urban trajectory database and is compared to several computational algorithms introduced in previous studies. The results show that our approach reduces uncertainty values when detecting trajectory stop points as well as a significant improvement of the recall and precision values.