Understanding the behavior of charring or decomposing materials exposed to high temperature environments is an essential aspect in rocket design. In particular, the tip of re-entry vehicles and sacrificial rocket nozzle liners are both exposed to extremely high temperatures. This thesis is specifically concerned with better understanding the reaction of sacrificial rocket nozzle liners to these high temperature environments. The sacrificial liners are designed to shield the rocket nozzle from the thermal and chemical effects of the heated exhaust gas that flows through the nozzle. However, in the design process space and weight of the rocket are at a premium. The sacrificial liners need to be designed to be as light and thin as possible, while properly shielding the nozzle from the heated exhaust gases. The sacrificial liner material is initially impermeable in its virgin state; however, as the liner is exposed to the heated exhaust gases, it chars and the liner material begins to decompose. The decomposition of the liner by heating in the absence of oxygen is known as pyrolysis. At high temperatures, the virgin material will decompose into a solid material (charred liner) and a vapor (pyrolysis gas). The pyrolysis process leads to the flow of pyrolysis gases throughout the porous charred liner. As a result, significant pressures can build within the liner. If the pressures within the liner are high enough, mechanically weak portions of the liner may fracture and break off. Fracturing of the liner could expose the nozzle to the heated exhaust gases, thus jeopardizing the structural integrity of the nozzle. Therefore, it is important to understand the pressure distribution within the sacrificial liners that occurs as a result of the pyrolysis process. This work describes the code PorePress, which solves for steady state and transient pressure distributions in 1- and 2-D axisymmetric geometries that represent sacrificial liners. The PorePress code is essentially a 1- and 2-dimensional differential equation solver for mixed, unstructured geometries. Specifically, the code is used for solving a coupled form of the Ideal Gas Law, Conservation of Mass, and Conservation of Momentum Equations, which describe the flow and resulting pressures within liner geometries. The code centers around using Taylor Series expansions to approximate derivatives needed to solve the appropriate differential equations. The derivative approximation process used in PorePress is grid transparent, meaning the same method can be used for any combination of quadrilateral (4-sided) or triangular (3-sided) elements in a mesh, without any changes to the code. Stability issues arise in both the 1- and 2-D PorePress solution processes, as a result of the non-linear nature of the coupled equations, high spatial gradients, and large variations in material properties. In the 1-D case stabilization techniques such as: upwinding, dynamic differencing, under-relaxation, and preconditioning are applied. Meanwhile, in the 2-D case, stabilization techniques such as: inverse weighting and QR factorization of the coefficient matrix, under-relaxation, and preconditioning are applied. The steady state and transient solution processes for both the 1- and 2-D pore pressure solution processes used in PorePress are covered in this thesis, as well as discussion of the resulting pressure distributions. Certain sacrificial liner design considerations that arise as a result of PorePress models for sample liner burns are also covered. / Master of Science