A number of robotic studies have recently turned to biological inspiration in designing control schemes for flexible robots. Examples of such robots include continuous manipulators inspired by the octopus arm. However, the control strategies used by an octopus in moving its arms are still not fully understood. Starting from a dynamic model of an octopus arm and a given set of muscle activations, we develop a simulation technique to characterize the stiffness throughout a motion and at multiple points along the arm. By applying this technique to reaching and bending motions, we gain a number of insights that can help a control engineer design a biologically inspired impedance control scheme for a flexible robot arm. The framework developed is a general one that can be applied to any motion for any dynamic model. We also propose a theoretical analysis to efficiently estimate the stiffness analytically given a set of muscle activations. This analysis can be used to quickly evaluate the stiffness for new static configurations and dynamic movements.