Elastic electron scattering cross sections from 5-30 eV are reported for the molecules C H C 2 H 6 , C 3 Hs, Si 2 H 6 , and GeH 4 , obtained using an implementation of the Schwinger 2 4' multichannel method for distributed-memory parallel computer architectures. These results, obtained within the static-exchange approximation, are in generally good agreement with the available experimental data. These calculations demonstrate the potential of highly parallel computation in the study of collisions between low-energy electrons and polyatomic gases. The computational methodology discussed is also directly applicable to the calculation of elastic cross sections at higher levels of approximation (target polarization) and of electronic excitation cross sections.