Form-finding analysis is carried out and presented for half-Costa tensioned membrane structure model in YZ-plane. There are three models presented, each with different center part of the half-Costa boundaries. Nonlinear analysis method is adopted for the form-finding analysis. Half-Costa tensioned membrane models in YZ-plane with different geometry have been found in a good agreement with least square error of total warp and fill stress deviation. Results obtained from this study would become a reference to select suitable parameters to increase the performance of sustainable tensioned membrane structure in the form of half-Costa in YZ-plane respected to their boundary condition. These resource efficient structures have the ability to prevent further damage to the environment hence these models presented are good selective forms for design engineer and architect to ponder on.