We present a theoretical study for propagation of Lamb waves in cubic thin plates consisting of solid inclusions placed periodically in the host material. The dispersion curves of Lamb waves propagating parallel to the surfaces of the plates are calculated based on the plane wave expansion method for triangular lattices. We realize the existence of full band gaps in the systems composed of W cylinders embedded in a Si matrix with filling ratio f = 0.176 for different thickness ratios of h/a, where h is the plate thickness and a is the lattice spacing.