FINESSE is a software simulation allowing one to compute the optical properties of laser interferometers used by interferometric gravitational-wave detectors today. This fast and versatile tool has already proven to be useful in the design and commissioning of gravitational-wave detectors. The basic algorithm of FINESSE numerically computes the light amplitudes inside an interferometer using Hermite-Gauss modes in the frequency domain. In addition, FINESSE provides a number of commands for easily generating and plotting the most common signals including power enhancement, error and control signals, transfer functions and shot-noise-limited sensitivities. Among the various simulation tools available to the gravitational wave community today, FINESSE provides an advanced and versatile optical simulation based on a general analysis of user-defined optical setups and is quick to install and easy to use. PACS numbers: 04.80. Nn, 95.55.Ym, 07.60.Ly, 42.25.Hz