Matrix variational calculations, reported previously, of e-He inelastic scattering, have been extended into the near-threshold regions for excitation of the metastable states 2S3 and 2S1. Wigner cusp and rounded-step structures are computed at these thresholds for elastic and inelastic processes not involving the threshold channels. Excitation cross sections are computed for the threshold channels. The present computed results are compared with available experimental data, and found to be in general qualitative and quantitative agreement. A new estimate is derived of the rate coefficient for deactivation of He(2S3) by thermal electrons: a constant value 2.525 × 10-9 cm3/sec for T≤1053 °K. © 1975 The American Physical Society.