A derivation is presented for X(t),the transformed fraction as a function of time, in a phase transformation process which produces randomly oriented anisotropic particles. The key novel element in the development and results is the inclusion of blocking (shielding) effects. The derivation is performed for a 2D system in which symmetrical particles of arbitrary shape are formed. In addition, approximate calculations are performed for X(t) for the case of elliptical particles in order to estimate the influence of growth rate anisotropy upon the magnitude of the blocking effects.