In this effort the effect of Rydberg electronic excitation on the structure of cyclic and polycyclic alkanes is investigated. Two-photon resonant, one-photon ionization, mass-resolved excitation spectroscopy is employed to observe the (sigma 3s)<--(sigma)(2) Rydberg transitions of cyclohexane, bicyclo[2.2.2]octane, and adamantane cooled in a supersonic jet expansion. Rydberg spectra of these three molecules display sharp, well-resolved vibronic structure. Analysis of the spectra is assisted by isotopic substitution, circular/linear polarization, vibronic feature widths (rotational selection rules), as well as comparison to the ground-state vibrational energies. A significant reduction of vibrational energies in the excited electronic state and a 381 cm(-1) blue shift of the transition origin upon deuterium isotope substitution for cyclohexane are interpreted as due to the promotion of an electron from a sigma-bonding orbital to a nonbonding Rydberg orbital upon optical excitation. Extensive vibronic coupling is observed for both cyclohexane and adamantane in their excited (sigma 3s) Rydberg electronic states. Jahn-Teller splitting is small for adamantane but quite substantial for cyclohexane. This difference is attributed to the basic stability difference for the two different ring systems (mono- and tri-cyclic). A progression in a nontotally symmetric mode is observed in the Rydberg spectrum of bicycl[2.2.2]octane suggesting a change in the geometry of this molecule upon (sigma 3s)<--(sigma)(2) excitation.