There exist 16 symmetry classes of piezoelectric materials. Of these, the two transverse isotropic classes are physically most interesting. The piezoelectric tensors with at least transverse isotropic symmetry form a 3-dimensional linear space. We consider homogeneous and transverse isotropic random fields taking values in the above space. It turns out that such a field has 4 spectral densities. We deduce the spectral expansion of the field in terms of stochastic integrals with respect to scattered random measures. Based on the obtained expansion, we propose a novel Monte Carlo simulation algorithm.