The spherical tearing mode is the three-dimensional analog of the classical tearing mode in two dimensions. In three dimensions, loops of field lines connecting magnetic nulls play the role of separatrices. A numerical study of the tearing instability of a three-dimensional analytic equilibrium containing a closed spherical tearing surface composed of null-null lines is presented. A new fast tearing instability is identified. Implications of this model for global models of reconnection at the dayside magnetopause are discussed.