We report cross sections for elastic electron scattering by gas phase glycine (neutral form), obtained with the Schwinger multichannel method. The present results are the first obtained with a new implementation that combines parallelization with OpenMP directives and pseudopotentials. The position of the well known π* shape resonance ranged from 2.3 eV to 2.8 eV depending on the polarization model and conformer. For the most stable isomer, the present result (2.4 eV) is in fair agreement with electron transmission spectroscopy assignments (1.93 ± 0.05 eV) and available calculations. Our results also point out a shape resonance around 9.5 eV in the A' symmetry that would be weakly coupled to vibrations of the hydroxyl group. Since electron attachment to a broad and lower lying σ* orbital located on the OH bond has been suggested the underlying mechanism leading to dissociative electron attachment at low energies, we sought for a shape resonance around ~4 eV. Though we obtained cross sections with the target molecule at the equilibrium geometry and with stretched OH bond lengths, least-squares fits to the calculated eigenphase sums did not point out signatures of this anion state (though, in principle, it could be hidden in the large background). The low energy (~1 eV) integral cross section strongly scales as the bond length is stretched, and this could indicate a virtual state pole, since dipole supported bound states are not expected at the geometries addressed here.