The multidimensional geometric effects within the heat shield of the Stardust sample return capsule are studied over its reentry trajectory, using a material response solver. The solver models material charring, conductive heat transfer, surface energy balance, pyrolysis gas transport, and orthotropic material properties in three dimensions. The material response of the heat shield is computed using isotropic and orthotropic models for conductivity and permeability, and both results are compared to the 1-D model. The orthotropic and isotropic models predict dissimilar responses, especially in regard to the surface blowing rates and pyrolysis gas transport. Although both models yield similar results for the surface temperature near the stagnation region, the temperature distribution within the heat shield differs. The 1-D model appears to greatly underestimate the thermal response deeper in the material, especially late in the trajectory.