We report on elastic integral, momentum transfer, and differential cross sections for collisions of low-energy electrons with thiophene molecules. The scattering calculations presented here used the Schwinger multichannel method and were carried out in the static-exchange and static-exchange plus polarization approximations for energies ranging from 0.5 eV to 6 eV. We found shape resonances related to the formation of two long-lived π∗ anion states. These resonant structures are centered at the energies of 1.00 eV (2.85 eV) and 2.82 eV (5.00 eV) in the static-exchange plus polarization (static-exchange) approximation and belong to the B1 and A2 symmetries of the C2v point group, respectively. Our results also suggest the existence of a σ∗ shape resonance in the B2 symmetry with a strong d-wave character, located at around 2.78 eV (5.50 eV) as obtained in the static-exchange plus polarization (static-exchange) calculation. It is worth to mention that the results obtained at the static-exchange plus polarization level of approximation for the two π∗ resonances are in good agreement with the electron transmission spectroscopy results of 1.15 eV and 2.63 eV measured by Modelli and Burrow [J. Phys. Chem. A 108, 5721 (2004)]. The existence of the σ∗ shape resonance is in agreement with the observations of Dezarnaud-Dandiney et al. [J. Phys. B 31, L497 (1998)] based on the electron transmission spectra of dimethyl(poly)sulphides. A comparison among the resonances of thiophene with those of pyrrole and furan is also performed and, altogether, the resonance spectra obtained for these molecules point out that electron attachment to π∗ molecular orbitals is a general feature displayed by these five-membered heterocyclic compounds.