TUNNELING SPLITTINGS IN MODEL 2D POTENTIALS .1. V(X, Y) = V(0)(Y(2)-Y(0)2)(2)+1 2-OMEGA(1)2X(2)+1/4-ALPHA-X(4)+CX(2)Y(2)/

We propose a semiclassical method for calculating tunneling splittings , DELTA(n1n2), of the vibrationally excited states in 2D 'squeezed' po tential. Semiclassical wavefunctions in the classically forbidden regi on are found in the vicinity of the extreme real trajectory in the inv erted potential, and 2D version of the Liftshitz' formula, which relat es splitting to the probability flux through the dividing plane, is em ployed to calculate DELTA(n1n2). Computations have been performed for different values of coupling strength and anharmonicity parameter. The results are compared with exact splittings and wavefunctions obtained by diagonalization of the 2D Hamiltonian. It is shown, that for small positive and arbitrary negative couplings the WKB method is accurate enough to reproduce correctly the change of tunneling splitting in pro gressions. WKB wavefunctions are in reasonable agreement with the exac t ones in this case. Disagreement shows up with increasing C > 0 for h igh vibrational levels, when extreme trajectories of other types can c ome into play.