This paper presents elasto-plastic limit analysis of reliability-based geometrically nonlinear topology optimization. For this purpose, by reason of uncertainties the volume fraction is considered randomly during optimization. Thus reliability-based design has been considered for solving the problems. To perform reliability-based topology optimization design, the Monte-Carlo simulation method has been applied to calculate the probability of failure, thus the reliability index. Besides, bi-directional evolutionary structural optimization (BESO) method is used to consider the effect of geometrically nonlinear design for elasto-plastic analysis. Plastic behavior is controlled by applying a bound on the plastic limit load multipliers using limit analysis. The adequacy of the proposed method is exhibited by three 2D benchmark problems. 2D models of L-shape beam and U-shaped plate are considered for reliability-based design and geometrically nonlinear analysis topology optimization in case of elastic material. Additionally, 2D and 3D elasto-plastic material models have been considered to demonstrate that the proposed method can find the optimal topology of elasto-plastic models for reliability-based design and geometrically nonlinear analysis.