The paper focuses on the stiffness modeling of a new type of compliant manipulator and its non-linear behavior under external loading. The manipulator under study is a serial mechanical structure composed of dual-triangle segments. The main attention is paid to the possible equilibriums and the manipulator stiffness behavior under the loading for the initial non-straight configuration. It was demonstrated that there is a quasi-buckling phenomenon for this manipulator while the external loading increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced Virtual Joint Method (VJM). Relevant simulation study confirmed the obtained theoretical results.