For interstellar missions, directed energy is envisioned to drive wafer-scale spacecraft to relativistic speeds. Spacecraft propulsion is provided by a large array of phase-locked lasers, either in Earth orbit or stationed on the ground. The directed-energy beam is focused on the spacecraft, which includes a reflective sail that propels the craft by reflecting the beam. Fluctuations and asymmetry in the beam will create rotational forces on the sail, so the sail geometry must possess an inherent, passive stabilizing effect. A hyperboloid shape is proposed, since changes in the incident beam angle due to yaw will passively counteract rotational forces. This paper explores passive stability properties of a hyperboloid reflector being bombarded by directed-energy beam. A 2D cross-section is analyzed for stability under simulated asymmetric loads. Passive stabilization is confirmed over a range of asymmetries. Realistic values of radiation pressure magnitude are drawn from the physics of light-mirror interaction. Estimates of beam asymmetry are drawn from optical modeling of a laser array far-field intensity using fixed and stochastic phase perturbations. A 3D multi-physics model is presented, using boundary conditions and forcing terms derived from beam simulations and lightmirror interaction models. The question of optimal sail geometry can be pursued, using concepts developed for the baseline hyperboloid. For example, higher curvature of the hyperboloid increases stability, but reduces effective thrust. A hyperboloid sail could be optimized by seeking the minimum curvature that is stable over the expected range of beam asymmetries.