We propose a least-action variational method to determine the optimal tunneling paths in multidimensional polyatomic reactions on the basis of the minimum energy path (MEP) and the least motion path (LMP). Taking into account geometrical features of the MEP (i.e., variations of path tangent and path curvature or variations of reaction plane along the MEP), the tunneling path is determined to minimize the amount of exponential damping of the nuclear wave function in the passage through the classically forbidden region. As a demonstration, the method is applied to a polyatomic reaction, NH3+OH-->NH2+H2O, in which there are highly curved regions on the MEP before and after a transition state. It is shown that the imaginary action integral calculated along the variationally determined tunneling path decreases extensively in comparison with that calculated along the MEP. (C) 1997 American Institute of Physics.