A computational approach for fitting sedimentation velocity experiments from an analytical ultracentrifuge in a model-independent fashion is presented. This chapter offers a recipe for obtaining high-resolution information for both the shape and the molecular weight distributions of complex mixtures that are heterogeneous in shape and molecular weight and provides suggestions for experimental design to optimize information content. A combination of three methods is used to find the solution most parsimonious in parameters and to verify the statistical confidence intervals of the determined parameters. A supercomputer implementation with a MySQL database back end is integrated into the UltraScan analysis software. The UltraScan LIMS Web portal is used to perform the calculations through a Web interface. The performance and limitations of the method when employed for the analysis of complex mixtures are demonstrated using both simulated data and experimental data characterizing amyloid aggregation.