State-resolved collision energy dependence of Penning ionization cross sections of acetylene (C2H2) and ethylene (C2H4) with He*(2 3S) metastable atoms was observed in a wide collision energy range from 20 to 350 meV. A recently developed discharge nozzle source with a liquid N2 circulator was employed for the measurements in the low-energy range from 20 to 80 meV. Based on classical trajectory calculations for the energy dependence of the partial ionization cross sections, anisotropic potential energy surfaces for the present systems were obtained by optimizing ab initio model potentials for the chemically related systems Li+C2H2 and C2H4. In the case of C2H2, the global minimum was found to be located around the H atom along the molecular axis with a well depth of 48 meV (ca. 1.1 kcal/mol). On the other hand, a dominant attractive well with a depth of 62 meV (ca. 1.4 kcal/mol) was found in the piCC electron region of C2H4. These findings were discussed in connection with orbital interactions between molecular orbitals of the target molecules and atomic orbitals of the metastable atom. It is concluded that sigma-type unoccupied molecular orbitals of C2H2 and a piCC-type highest occupied molecular orbital of C2H4 play a significant role for the attractive-site preference of sigma direction in C2H2 and pi direction in C2H4, respectively.