Abstract: The coiled configuration of flexible reflector antennas is difficult to predict due to the geometrically nonlinear large deformations that occur during coiling stowage. To address this challenge, a self-consistent solution method based on Bayesian optimization was proposed in this study. First, based on the Euler–Bernoulli beam theory, the mechanical equilibrium differential equations governing the spiral coiling of a single-petal reflector were established, characterizing the relationship between the applied loads and the stowed configuration. Then, to resolve the complex implicit relationships between the boundary parameters and the coiled configuration in this high-order boundary-value problem, Bayesian optimization was introduced to construct a self-consistent framework, in which a Gaussian process surrogate model was employed to efficiently identify the boundary parameters that satisfy the geometric continuity constraints. Finally, the proposed method was validated through finite element simulations. The results show that the relative deviation of the coiling radius between theoretical predictions and simulation results is within 1.5%, demonstrating the effectiveness of the proposed method in coiled configuration prediction and stress state analysis. The proposed method provides theoretical support for the structural design and stowage analysis of flexible reflectors.