This dataset shows the original data of a series of enhanced-gravity (centrifuge) analogue models, which were performed to test the influence of the pre-existing fabrics in the brittle upper crust on the evolution of structures resulting from oblique rifting. The obliquity of the rift (i.e., the angle between the rift axis and the direction of extension) was kept constant at 30° in all the models. The main variable of this experimental series was the orientation of the pre-existing fabrics (indicated as the angle between the trend of the fabric and the orthogonal to extension), which varied from 0° to 90° (i.e., from orthogonal to parallel to the extension direction). The inherited discontinuities were reproduced by cutting with a knife through the top brittle layer of models. An overview of the experimental series is shown in Table 1. In this dataset, four different data types are provided for further analysis: 1) Top-view photos of model deformation, taken at different time intervals and showing the deformation process of each model; they can be used to interpret the geometrical characteristics of rift-related faults; 2) Digital Elevation Models (DEMs) used to reconstruct the 3D deformation of the analogue models, allowing for quantitative analysis of the fault pattern. 3) Movies of model deformation, built from top-view photos, which help to visualize the evolution of model deformation; 4) Faults line-drawings to be used for statistical quantification of rift-related structures. Further information on the modelling strategy and setup can be found in the publication associated to this dataset and in Corti (2012), Philippon et al. (2015), Maestrelli et al. (2020), Molnar et al. (2020), Zwaan et al. (2021), Zou et al. (2023). Materials used to perform these enhanced-gravity analogue models were described in Montanari et al. (2017), Del Ventisette et al. (2019) and Zwaan et al. (2020).