A numerical method, called multiple monopole (or multipole) method, based on the Generalized Multipole Technique (GMT) is proposed to calculate the band structures of vector waves in two-dimensional solid-solid phononic crystals which are composed of arbitrarily shaped cylinders embedded in a host medium. In order to find the eigenvalues (eigenfrequency) of the problem, besides the sources used to expand the wave field, an extra monopole source is introduced which acts as the external excitation. By varying the frequency of the excitation, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and sweeping the boundary of the irreducible first Brillouin zone, the band structure can be obtained. Some numerical examples are presented to validate the proposed method.