The ground structure method is used to find an optimal solution for the layout optimization problem. The problem domain is discretized with a union of highly connected members, which is called a ground structure. The objective typically is to minimize the total volume of material while satisfying nodal equilibrium constraint and predefined stress limits (plastic formulation). However, such approach may lead to very slender members and unstable nodes that might cause instability issues. This thesis presents the implementation of the ground structure method involving instability consideration. The plastic formulation is implemented considering buckling constraint and nodal instability constraint either in isolation or in combination. The Euler buckling criteria is taken as the buckling constraint in the implementation with local instability consideration. The nominal lateral force method is used in the implementation involving nodal instability consideration. Moreover, the efficiency of the nonlinear programming is addressed. Several numerical examples are presented to illustrate the features of the implementation.