ellc analyzes the light curves of detached eclipsing binary stars and transiting exoplanet systems. The model represents stars as triaxial ellipsoids, and the apparent flux from the binary is calculated using Gauss-Legendre integration over the ellipses that are the projection of these ellipsoids on the sky. The code can also calculate the fluxweighted radial velocity of the stars during an eclipse (Rossiter-McLaghlin effect). ellc can model a wide range of eclipsing binary stars and extrasolar planetary systems, and can enable the use of modern Monte Carlo methods for data analysis and model testing.