This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.