Immune stimulating complex (ISCOM) particles consisting of a mixture of Quil-A, cholesterol, and phospholipids were structurally characterized by small-angle x-ray scattering (SAXS). The ISCOM particles are perforated vesicles of very well-defined structures. We developed and implemented a novel (to our knowledge) modeling method based on Monte Carlo simulation integrations to describe the SAXS data. This approach is similar to the traditional modeling of SAXS data, in which a structure is assumed, the scattering intensity is calculated, and structural parameters are optimized by weighted least-squares methods when the model scattering intensity is fitted to the experimental data. SAXS data from plain ISCOM matrix particles in aqueous suspension, as well as those from complete ISCOMs (i.e., with an antigen (tetanus toxoid) incorporated) can be modeled as a polydisperse distribution of perforated bilayer vesicles with icosahedral, football, or tennis ball structures. The dominating structure is the tennis ball structure, with an outer diameter of 40 nm and with 20 holes 5-6 nm in diameter. The lipid bilayer membrane is 4.6 nm thick, with a low-electron-density, 2.0-nm-thick hydrocarbon core. Surprisingly, in the ISCOMs, the tetanus toxoid is located just below the membrane inside the particles.