A theoretical analysis of fiber Bragg grating (FBG)-based plane strain monitoring of aerostat envelope structures is presented. Plane strain analysis of FBG-based aerostat envelope structures is much more complex than the case along the axis of the optical fiber because the effect of transverse stress on the FBG should be taken into consideration. To achieve accurate strain measurement of the aerostat envelope, a theoretical model is set up by using two perpendicular fibers in the monitoring. An analytical formula that evaluates the relationship between the strain measured by FBG sensors and the real one in the aerostat envelope is established. On the other hand, the real strain of aerostat envelope strain is affected by two unknown parameters, axial transfer rate K(L) and the radial transfer rate K(R). An equation is derived to calculate the axial transfer rate K(L). Then, the finite element method results show that K(R) is a very small value, but it cannot be ignored in accurate measurement. This paper would lay a theoretical groundwork for the research and design of FBG sensors in the structural health monitoring of aerostat envelope structures.