Recent efforts in soft-body control have been hindered by the infinite dimensionality of soft bodies. Without restricting the deformation space of soft bodies to desired degrees of freedom, it is difficult, if not impossible, to guarantee that the soft body will remain constrained within a desired operating range. In this article, we present novel modeling and fabrication techniques for leveraging the reorientation of fiber arrays in soft bodies to restrict their deformation space to a critical case. Implementing this fiber reinforcement introduces unique challenges, especially in complex configurations. To address these challenges, we present a geometric technique for modeling fiber reinforcement on smooth elastomeric surfaces and a two-stage molding process to embed the fiber patterns dictated by that technique into elastomer membranes. The variable material properties afforded by fiber reinforcement are demonstrated with the canonical case of a soft, circular membrane reinforced with an embedded, intersecting fiber pattern such that it deforms into a prescribed hemispherical geometry when inflated. It remains constrained to that configuration, even with an additional increase in internal pressure. Furthermore, we show that the fiber-reinforced membrane is capable of maintaining its hemispherical shape under a load, and we present a practical application for the membrane by using it to control the buoyancy of a bioinspired autonomous underwater robot developed in our lab. An additional experiment on a circular membrane that inflates to a conical frustum is presented to provide additional validation of the versatility of the proposed model and fabrication techniques.