The non-linear, partial differential equations of magnetohydrodynamics are iterated simultaneously by computer to determine the time development of a single sunspot. Axisymmetry and incompressibility are assumed. The initial conditions are (1) zero velocity everywhere, and (2) the magnetic-field distribution of a ring current embedded in the photosphere. The initial magnetic field is then allowed to relax by magnetic diffusion and by the creation of a velocity field. It is shown that (1) Evershed motion outward from the sunspot will develop from reasonable initial parameters, and (2) the growth rate of the magnetic configuration depends on the strength of the initial magnetic field.