The trapped equatorial standing modes described theoretically by Gent (1979) are reproduced in a single vertical-mode numerical ocean model. integrations are carried out in domains whose longitudinal extents are characteristic of the widths of the Atlantic and Pacific Oceans, as well as in a narrow ocean in which the simplest possible standing mode can exist. The modes are shown to be very insensitive to small changes in basin width and to the inclusion of friction, and somewhat sensitive to the inclusion of the nonlinear terms and to rotation of the rectangular basin relative to the equator. Moreover, they arise spontaneously from simple atmospheric forcing or from random initial conditions. Typically, 20–40% of the energy input to the equatorial ocean remains trapped in a number of distinct standing modes after about nine years of integration time. The wider the ocean domain, the more energy remains trapped near the equator. These unexpected results have important implications for equatorial ocean dynamics and tropical air-sea interaction.