Solid particles can adhere to fluid interfaces, modifying interfacial properties such as the surface tension and the surface elasticity. We here describe a new simulation method, the Fast Interface Particle Interaction (FIPI) method, capable of simulating on commodity hardware up to 100k particles interacting with fluid interfaces of complex morphology. The method is based on resolving interfacial and hydrodynamic length scales larger than the particle, and model particle-level phenomena with physically consistent algebraic models. For its ability to simulate large numbers of potentially very small particles, FIPI represents a useful tool for investigating phenomena of particle adsorption/desorption and particle-induced surface tension modification in problems of froth flotation, drop/foam stabilisation, Bijelformation and other multiphase systems. Program summary: Program Title: FIPI Licensing provisions: GPLv2 Programming language: C++ Nature of problem: Simulation of particle-laden fluid interfaces (3-phase flows) Solution method: Spectral method Running time: Up to dozens of hours on a single processor