A new empirical many-body potential energy function (PEF) is proposed, which comprices two- and three-body atomic interactions. The two-body potential is a kind of hybrid function and the three-body potential is formed by additive and nonadditive functions. The additive part is expressed in terms of two-body interactions, and the nonadditive part is expressed as triple-dipole function. The PEF satisfies bulk cohesive energy, bulk stability condition, and bulk modulus. The PEF is parameterized for gold, silver, and copper elements in fc.c. crystal structure. The elastic constants of the elements are calculated, and the structural stability and energetics of microclusters containing 3 to 7 atoms of the same elements are investigated. The calculated elastic constants are in good agreement with experimental values, and the most stable microcluster geometries are qualitatively in agreement with the available literature data.