The volume-of-fluid (VOF) method is among the most popular methods of simulating fluid saturation in porous media. Unfortunately, however, the VOF method becomes extremely slow in 3D domains. The problem arises from the need to use very small time steps and volume elements to achieve an accurate and stable numerical simulation. A quasi-static alternative to approximate the results of VOF simulations is the pore morphology method (PMM). The PMM does not require solving nonlinear partial differential equations (i.e., the Navier–Stokes equations), and as such, it is orders of magnitude faster than the VOF method in terms of CPU time. However, the PMM is less accurate than the VOF or other physics-based methods. The current study was therefore devised to assess the accuracy of PMM simulations in geometries with different degrees of anisotropy and disorder. Our study revealed that the PMM predictions become inaccurate when the pores in the media have high-aspect-ratio cross sections (e.g., rectangular cross sections). It was also found that the PMM algorithm marks the largest pore in the domain as the location where a non-wetting phase starts penetrating into the saturated media regardless of the contact angle of the media (as long as all solid surfaces in the media have the same contact angle), which obviously is inaccurate. The PMM results reported in this paper were produced by using an in-house MATLAB code.