Terrestrial laser scanning technology enables the rapid acquisition of dense point clouds in a very short time. Thanks to this, we obtain a quasi-continuous surface model that accurately reflects the current shape of the measured object. This technology is particularly useful for monitoring deformations of curved surfaces, such as vaults, tunnels, and chimneys. However, assessing deformations in such objects requires not only appropriate data acquisition but also rigorous data processing and visualization. An additional consideration is the method used to define deformations—either as differences between measurement epochs or as geometric deviations from design documentation. This article presents methods for determining changes in surface geometry, relative to design data (main cross-section parameters), for curved objects. Point clouds acquired via terrestrial laser scanning were used as measurement data. Two approaches are discussed: one involving a comparison between the point cloud and a three-dimensional theoretical model of the object, and another based on projecting the point cloud onto a plane and comparing it to a reference surface derived from design data. The advantages and limitations of each approach are outlined. The significant potential of point cloud processing is also highlighted, both in terms of visualization and interpretation of TLS data.