Parametric digital modelling is today at the centre of architectural designers and critics interests. Increasing potentialities and developments of hardware and software allow to apply parametric methods in the whole design process. But the definition of “Architettura Parametrica” has an older origin: it was coined by Luigi Moretti in the Forties. Moreover, some examples of parametric thinking were found by several scholars almost since the origin of architectural history. This research arises as a development of previous studies, carried on by the authors, adopting parametric digital modelling for a classification of shapes and their possible combinations. The research aims to apply this method for the definition and description of the formal elements used for the construction of system of complex historical vaults. While in form-making practices, shape-grammar studies represent a consolidated and systematic methodology that can open interesting research developments, in the specific case of the re-construction of complex vault systems, this refers to the study of continuous surfaces and their grammar, as well as to a relations’ syntax that connect them. These latter considerations, which are related to a grammatical and syntactic structure of vaults, not only had a remarkable influence on the parametric model’s construction, but they also offer a valid starting point for the definition of a repeatable methodology that could be used to study several complex vault systems; this aspect could also be one of the most prominent developments of the present research. This method has been tested on several case studies of Baroque vaulted atria and deepened for the specific case of lunettes dome in the atrium of Palazzo Carignano in Turin, Italy.