It has been suggested that joint stiffness plays a fundamental role in understanding how CNS controls wrist rotations. In a previous work, we estimated passive wrist stiffness in combinations of flexion-extension (FE) and radial-ulnar deviation (RUD) using a robot for wrist rehabilitation. In that work, we linearized the FE-RUD torque/angle field at the neutral position to obtain 2-DOF stiffness tensors. While that method provided very useful information about the characteristics of the wrist stiffness, it forces the results to be symmetrical about the origin of the reference frame, making them dependent on the choice of the neutral position. In this paper, we propose an alternative method to estimate the elastic potential energy of the wrist joint, based on the basis fields approximation approach [1]. This algorithm is capable of capturing the non-linearities of the angle-torque fields and it is not sensitive to the choice of the reference frame. Results on 4 subjects confirm previous findings that the movement of least stiffness goes from radial-extension to ulnar-flexion, known as the “dart-throwers motion” moreover, we show that the 2-D elastic field of the wrist is not linear about the neutral position. While this last result has been previously showed only in pure FE or RUD, here we present a method to characterize it in combinations of FE and RUD, thus allowing to better model general wrist rotations.