An arched structure provides an effective load carrying system for large span structures. When it comes to long span roof structures, timber arches are one of the best solutions from both structural and aesthetical point of view. Glulam arched structures are often designed using slender elements due to economic consideration. Such slender cross-section shape increases the risk of instability. Instability analysis of straight members such as beam and column are explicitly defined in Eurocode. However, for instability of curved members no analytical approach is provided in the code, thus some numerical method is required. Nonetheless, an approximation is frequently used to obtain the effective buckling length for the arched structures in the plane of arches. In this master thesis a linear buckling analysis is carried out in Abaqus to obtain an optimal effective buckling length both in-plane and out-of-plane for circular glulam arched structures. The elastic springs are used to simulate the overall stiffness of the bracing system. The results obtained by the FE simulations are compared with a simple approximation method. Besides, the forces acting on the bracings system is obtained based on 3D geometric nonlinear stress analysis of the timber trusses. Our findings conclude that the approximation method overestimates the effective buckling length for the circular glulam arched structures. In addition, the study indicates that the position of the lateral supports along the length of the arch is an important design aspect for buckling behaviour of the arched structures. Moreover, in order to acquire an effective structure lateral supports are needed both in extrados and intrados. Furthermore, instead of using elastic spring elements to simulate the overall stiffness of the bracing system, a full 3D simulation of two parallel arches was performed. It was shown that the springs are stronger than the real bracing system for the studied arch.