Core-scale measurements are considered the ground truth that oil and gas or electric utility companies use to predict the migration of fluids such as oil, natural gas, carbon dioxide, or brine deep underground during their extraction or injection operations. To provide a greater understanding of petrophysical properties of low-permeability geologic formations such as shales and tight gas sandstones, this study introduces a novel core-analysis procedure. The technique follows conventional pressure-pulse-decay permeametry, where the pressure in an inlet chamber adjacent to a cylindrical core plug undergoes a rapid pressurization, the system is shut in, and the pressure reaches a new equilibrium. However, unlike a standard unidirectional pressure-pulse decay, the full-immersion pressure-pulse decay (Hannon 2019) applies a pressure disturbance to the entire outer surface area of the sample. This article covers the numerical simulator designed to model flow through an anisotropic porous sample in this scenario. The model assumes distinct but uniform permeabilities along the radial and axial directions of the cylindrical plug sample. When extracting a plug vertically (or perpendicular to bedding), the permeability along the radial direction associates with the horizontal permeability (i.e., parallel to bedding), whereas in the axial direction, flow occurs perpendicular to bedding (a vertical permeability). Investigations of these model outputs demonstrate an approximately 20-fold decrease in time to complete a full-immersion experiment compared with conventional pressure-pulse decay. Furthermore, the pressure-decay curves resulting from the full-immersion method have slightly different shapes than those resulting from other unidimensional transient methods. These differences begin to demonstrate that, under achievable experimental conditions, the analysis of pressure data from one full-immersion test could enable the simultaneous estimation of the apparent permeabilities parallel and perpendicular to bedding of a cylindrical sample in addition to its porosity. A follow-up article finalizes the proof of this capability with a parameter-estimation procedure and presents experimental verification through a proof-of-concept study. Described in greater detail in that article, the parameter estimator requires multiple forward simulations to analyze the data, which behooves minimizing the compute time for each simulation. By using an alternating direction implicit time-marching scheme and a structured but variably spaced grid, the numerical simulator built for this purpose provides a forward model output with suitable accuracy in approximately 0.5 seconds.