The paper centres on stability investigations of a glued-laminated timber (glulam) dome under several snow load conditions. The dome consists of a triangulated network of curved glulam beams, a decking supported by curved purlins, and a steel tension ring. The dome is represented by two different models. The first model is a rigid-jointed space frame composed of curved beam elements. The second model consists of straight beam elements, with rigid or flexible joints, and a bracing to simulate the lateral support of the beams provided by the decking. Two finite element methods are presented and used in the analyses: A nonlinear method that computes the buckling load and a combined nonlinear/linear eigenvalue method that provides estimates of the buckling load. The results presented include buckling pressures, buckling modes, effects of joint stiffness and bracing on the stability of the dome, and the status of the material prior to buckling.