The linear elastic constants for a dry Weaire-Phelan foam with bidisperse cell-size distribution are computed. This highly ordered structure has eight polyhedral bubbles in the unit cell : two pentagonal dodecahedra and six tetrakaidecahedra with twelve pentagonal faces and two hexagonal faces. Both dodecahedra have equal volume and all of the tetrakaidecahedra have equal volume, but these volumes are different for the bidisperse structures considered here. These volume constraints preserve the cubic symmetry of the Weaire-Phelan structure so that the elastic response is completely characterized by a bulk modulus kappa for volume compression and two shear moduli mu(1) and mu(2). The shear moduli can be combined to obtain an effective isotropic shear modulus <(mu)over bar>, which represents the shear response averaged over all orientations of the foam. For the monodisperse case, <(mu)over bar> = <0.8684T(V)over bar>(-1/3), where T is surface tension and (V) over bar is the average bubble volume. For bidisperse structures, <(mu)over bar> never differs from the monodisperse case by more than 0.5% and the mu(i) always lie within 4% of <(mu)over bar>. The pressure inside the dodecahedra is always greater than the pressure inside the tetrakaidecahedra even when the dodecahedra are larger.