We have revealed topological defects (TDs) of the angle of optical indicatrix (OI) orientation in a glass Li2B4O7 sample, which originate from the specific spatial distribution of optical birefringence caused by residual mechanical stresses. It has been found that the strength of TDs of the OI rotation angle is equal to ±1/2. Following from the experimental results, we have shown that the regions around the TDs of OI orientation are those of a 3D stressed state. We have formulated criteria for determining whether 2D or 3D distributions of the optical anisotropy parameters appear, based on the TDs of OI orientation. It has been shown that, in some particular cases, the regions with the TDs can testify the availability of a 2D stressed state. Besides, we have demonstrated experimentally that the TDs can appear for more than one projection in the case of 3D distributions of the OI parameters, which appear under bending of glass plates by a distributed load.