Strikingly different Coulomb explosion behavior under intense laser fields is shown between the cis and trans geometric isomers of dichloroethene using 40-fs pulses at 0.8 mu m. Although the fragment-ion distributions in the mass spectra did not aid in the identification of the geometric and positional isomers of the dichloroethenes, we found that the angular distributions of atomic ions were strongly dependent on the geometric structures. The angular distributions of chlorine ions, carbon ions, and protons were similar between 1,1- and cis-1,2-dichloroethene, whereas trans-1,2-dichloroethene showed a very sharp distribution of chlorine ions and quite different distributions of carbon ions and protons. The origin of the anisotropic ion angular distributions is the geometric selection of molecules in the tunnel-ionization process followed by a Coulomb explosion, although molecules are randomly oriented in the gas phase. The highly charged molecular ions exploded into pieces, and the direction of atomic-ion ejection was strongly correlated with the relative configuration of atoms with respect to the electron-extraction axis, the repulsion with adjacent atomic ions within the molecule, and the degree of the persistence of a molecular frame. We propose herein that the most probable electron-extraction axis by tunneling, which is governed by the configuration of molecular orbitals, is different among three dichloroethene isomers. Because multiple ionization under intense laser fields occurs by sequential tunneling processes, the first ionization step at the leading edge of the laser pulse dominates the further ionization steps. Therefore, the shapes of the highest occupied molecular orbitals and probably the underlying orbitals determine the anisotropic emission of atomic ions that can be used to identify isomers.