We derive explicit expressions for the three 2 × 2 generalized Barnett-Lothe tensors S, H and L associated with the anti-plane deformations of monoclinic piezoelectric materials with symmetry plane at x3 = 0 and with poling in the x3-direction. The resulting generalized Barnett-Lothe tensors contain four independent components which are, in turn, expressed explicitly in terms of the ten electroelastic constants as well as the sum and product of the two Stroh eigenvalues. Concise and elegant expressions are obtained for the generalized Barnett-Lothe tensors for orthotropic piezoelectric materials.