Heatshield design and analysis has traditionally been a decoupled process, the designer creates the geometry generally without knowledge about how the design variables affect the thermostructural response or how the system will perform under off nominal conditions. Heatshield thermal and structural response analyses are generally performed as separate tasks where the analysts size their respective components and feedback their results to the designer who is left to interpret them. The analysts are generally unable to provide guidance in terms of how the design variables can be modified to meet geometric constraints and not exceed the thermal or structural design specifications. In general, the thermal response analysis of ablative thermal protection systems has traditionally been performed using a one-dimensional finite difference calculation. The structural analyses are generally one, two, or three-dimensional finite element calculations. In this dissertation, the governing differential equations for ablative thermal response are solved in three-dimensions using the finite element method. Darcy' Law is used to model the flow of pyrolysis gas through the ablative material. The three-dimensional governing differential equations for Darcy flow are solved using the finite element method as well. Additionally, the equations for linear elasticity are solved by the finite element method for the thermal stress using temperatures directly from the thermal response calculations. This dissertation also links the analysis of thermal protection systems to their design. The link to design comes from understanding the variation in the thermostructural response over the range of the design variables. Material property sensitivities are performed and an optimum design is determined based on a deterministic analysis minimizing the design specification of bondline temperature subject to appropriate constraints. A Monte Carlo simulation is performed on the optimum design to determine the probability of exceeding the design specifications. The design methodology is demonstrated on the Orion Crew Exploration Vehicle's compression pad design.