The conventional analysis of the circulator usually ignores ferrite disk thickness by assuming no axial variation, where the outcomes are limited to the case of small thickness ferrite disks. However, a typical scenario of a stripline Y-junction circulator has a ferrite disk thickness equal to that of the substrate. As a result, the assumption of a constant field along the feed-linewidth does not account for a realistic boundary condition. Increasing the ferrite thickness results in a significant variation in the field along the perimeter of the ferrite disk, which must be considered for accurate modeling and analysis. In this article, modeling of the Y-junction stripline circulator is proposed and investigated using Gaussian field distribution (GFD) boundary conditions. The proposed analysis takes into account the effects of ferrite thickness that controls both the field distribution and the demagnetization factor. The proposed analysis is applied to the case of a single ferrite disk and validated through a comparison between the analytical and simulation results conducted using a 3-D electromagnetic solver in different frequency bands. An excellent agreement is observed between the simulated and analytical results, highlighting the limitations of the conventional analysis methodology.