This study deals with the evaluation of the compliance map variability of a flexible structure using an active material, namely a shape memory alloy (SMA). Compliance or stiffness maps are an important indicator of the performances of robotic structures or mechanisms, for instance to assess the positioning error for a production task. The paper carefully examines the impact of the combination of a compliant structure (here a closed-loop flexible structure) and a SMA spring. Various static compliance maps are simulated and analyzed with respect to the state of the SMA. Several aspects are discussed, such as the concept of pseudo-workspace deriving from the deformation of the structure, or the anisotropy and non-linearity of the compliance change, as well as the relevance of the large displacement framework (in the strength of materials sense) for the correct calculation of the compliance maps. The results enable us to validate the capability of the combination of a compliant structure and a SMA component to achieve variable compliance maps that could be used for polyvalent robotic tasks.