We report several calculations of the differential, integral, and momentum-transfer cross sections for elastic scattering, and of the absorption cross sections (for the sum of all electronically inelastic and ionization processes) for electron-He collisions at 30-400 eV. We consider two basically different approaches to include the effect of absorption, i.e., loss of flux from the initial channel. The first is the matrix effective potential (MEP) based on a variational calculation of the polarization potential; this models absorption by including a pseudochannel whose properties are based on a variational adiabatic polarization potential. This method predicts both the absorption and elastic cross sections. The second method involves phenomenological absorption (A) potentials, calibrated against experimental absorption cross sections. These potentials, when combined with static (S), exchange (E), and real polarization (P) potentials form an SEPA optical model potential that is used to predict the elastic cross sections. The MEP model based on the variational polarization potential predicts the absorption cross sections with an average absolute error of 28% at 30 and 50 eV, and 5% at 100-400 eV. It predicts the elastic integral cross sections with an average absolute error of 8% over the whole energy range. The SEPA models, including a nonadiabatic polarization potential, predict the elastic integral cross sections with average absolute errors of 12 or 6%, depending on the shape function (i.e., r dependence) of the absorption potential. The adiabatic approximation for polarization is less accurate than the nonadiabatic one, even when absorption effects are included. Five new calculations of the differential cross sections at each of five impact energies are compared to experimental results in detail.