The paper deals with the elastostatic modeling of a multi-link flexible manipulator based on the two-dimensional (2D) dual-triangle tensegrity mechanism and its nonlinear behavior under external loading. The main attention is paid to the static equilibriums and the manipulator stiffness behavior under the loading for the arbitrary initial configuration. It was proved that there is a quasi-buckling phenomenon for this manipulator while the external loading is increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced virtual joint method (VJM). A relevant simulation study confirmed the obtained theoretical results.