Ab initio computations using the MP2/cc-pVTZ method have been carried out to calculate the structures and relative energies of the different conformations of five bicyclic molecules including bicyclo[3.1.0]hexane, 3-oxabicyclo[3.1.0]hexane, 6-oxabicyclo[3.1.0]hexane, 3,6-oxabicyclo [3.1.0]hexane, and bicyclo[3.1.0]hexan-3-one. Theoretical ring-puckering potential energy functions (PEFs) in terms of the ring-puckering coordinate have been calculated for each of the molecules and these were compared to those determined experimentally from spectroscopic data. Each potential function is asymmetric and has an energy minimum corresponding to where the five membered ring is puckered in the same direction as the attached three-membered ring. In contrast to the experimental result, the calculations predict that bicyclo[3.1.0]hexane has a second shallow energy minimum. All of the other molecules have a single conformational minimum and their experimental and theoretical PEFs agree very well. The wave functions for the lower ring-puckering energy levels have been computed.