Tensegrity structures are lightweight structures, often deployable, consisting of axial members (rods and cables). One of their design problems is to determine the minimum member mass to support an external force under the buckling and yielding conditions. In the previous work, the deformation of the structure is not considered, and the equilibrium position is assumed to be known in advance. However, when the structure is subjected to an asymmetric force, for example, the equilibrium position is not obvious and is typically unknown. As a more realistic problem setting, this study discusses a minimal mass design considering the deformation by an asymmetric external force. The self-equilibrated configuration is chosen as the initial configuration for the optimization. The internal force at this configuration is called the prestress, and is often utilized to improve structural stability and stiffness. The problem setting in this paper also allows us to introduce the prestress in the design. Mechanical formulae considering the deformation without the prestress are first derived. A minimal mass design problem allowing the deformation can be formulated by using these formulae. The problem is a nonlinear problem with many variables, and requires proper initial estimates. The paper also addresses this issue by employing dynamical simulation. The prestress can be introduced by modifying the member force calculation in the above formulae. Numerical examples are conducted to show the efficiency of the proposed method.