The condition for the maximum directivity from a spherical radiator is presented and it is shown that this directivity index is 20 log N, whereNis the number of consecutive modes excited. For superdirectivity, the relationship among the expansion coefficients is particularly simple and a closed‐form expression for the beam‐pattern function results. Using this method, a high directivity may be obtained no matter how small the sphere is, provided that the prescribed velocity distribution is maintained. Examples of the resulting beam patterns are given.