Pulmonary embolism (PE) is a significant medical problem that results in over 300,000 fatalities per year. A common preventative treatment for PE is the insertion of a metallic filter into the inferior vena cava that traps thrombi before they reach the lungs. The goal of this work is to use methods of mathematical modeling and design optimization to determine the configuration of trapped thrombi that minimizes the hemodynamic disruption. The resulting configuration has implications for constructing an optimally designed vena cava filter. Computational fluid dynamics is coupled with a nonlinear optimization algorithm to determine the optimal configuration of a trapped model thrombus in the inferior vena cava. The location and shape of the thrombus are parametrized, and an objective function, based on wall shear stresses, determines the worthiness of a given configuration. The methods are fully automated and demonstrate the capabilities of a design optimization framework that is broadly applicable. Changes to thrombus location and shape alter the velocity contours and wall shear stress profiles significantly. For vena cava filters that trap two thrombi simultaneously, the undesirable flow dynamics past one thrombus can be mitigated by leveraging the flow past the other thrombus. Streamlining the shape of the thrombus trapped along the cava wall reduces the disruption to the flow but increases the area exposed to low wall shear stress. Computer-based design optimization is a useful tool for developing vena cava filters. Characterizing and parametrizing the design requirements and constraints is essential for constructing devices that address clinical complications. In addition, formulating a well-defined objective function that quantifies clinical risks and benefits is needed for designing devices that are clinically viable.