An important factor for the development of spinal degeneration, pain and the outcome of spinal surgery is known to be the balance of the spine. It must be analyzed in an upright, standing position to ensure physiological loading conditions and visualize load-dependent deformations. Despite the complex 3D shape of the spine, this analysis is currently performed using 2D radiographs, as all frequently used 3D imaging techniques require the patient to be scanned in a prone position. To overcome this limitation, we propose a deep neural network to reconstruct the 3D spinal pose in an upright standing position, loaded naturally. Specifically, we propose a novel neural network architecture, which takes orthogonal 2D radiographs and infers the spine's 3D posture using vertebral shape priors. In this work, we define vertebral shape priors using an atlas and a spine shape prior, incorporating both into our proposed network architecture. We validate our architecture on digitally reconstructed radiographs, achieving a 3D reconstruction Dice of 0.95, indicating an almost perfect 2D-to-3D domain translation. Validating the reconstruction accuracy of a 3D standing spine on real data is infeasible due to the lack of a valid ground truth. Hence, we design a novel experiment for this purpose, using an orientation invariant distance metric, to evaluate our model's ability to synthesize full-3D, upright, and patient-specific spine models. We compare the synthesized spine shapes from clinical upright standing radiographs to the same patient's 3D spinal posture in the prone position from CT.