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At sufficiently low density, quasi-two-dimensional electron systems in their ground state form Wigner solids. In previous studies of the ground-state energy of such systems (in the absence of an applied magnetic field), the finite extension of electron wave functions in the direction perpendicular to the interface plane has not been considered. The efFect of the 6nite width of envelope functions on the ground-state energy of quasi-two-dimensional Wigner solids is studied in this paper. We evaluate the total Coulomb energy using numerically efficient Jacobi 8-function methods, for a variety of assumed crystal structures. The ground-state energy is found to be rather sensitive to the envelope wave-function width but the crystal structure remains hexagonal.