Kresling origami structure typically consists of triangular panels and regular polygonal surfaces, where each triangular panel connects to two adjacent triangular panels and polygons along the edges, forming the mountain and valley creases. The Kresling pattern has advantageous properties such as ease of folding and deployment and multiple states of stability. Generally, a single-layered Kresling system exhibits bi-stability. This study examines the Kresling system with different twisting angles in two stable states, denoted as state 1 and state 2. In this research, the origami system has been simplified as a truss system. The optimization of this truss system is performed by minimizing the compliance under a constant compressive load applied at different nodes of the Kresling unit cell, with constraints on the system’s weight and the minimum and maximum cross-sectional areas of the bars. This study aims to investigate the impact of bar areas on the stiffness of the Kresling system. This study explores how the cross-sectional area of the bars influences the effective stiffness and strain energy of these systems. Based on this study, it has been observed that state 2 behaves opposite to state 1. In the context of optimization, in the case of state 1, considerably higher optimum effective axial stiffness can be achieved when the twisting angle is smaller. But, in the case of state 2, a similar objective can be achieved when the twisting angle is larger.