Absolute vibrationally elastic cross sections for e-GeH4 collisions have been determined for electrons of 1, 2, 2.5, 3, 5, 7.5, 10, 15, 20, 60 and 100 eV incidence energy over a scattering angular range of 10 degrees -130 degrees . The observed angular distributions correspond, at least qualitatively, to theoretical formulations using the continuum-multiple-scattering method, the parameter-free static-exchange-polarization approximation, and a multichannel Schwinger variational calculation. Vibrational excitation functions and the energy distribution of elastically scattered electrons reveal a shape resonance at about 2-2.5 eV. Calculations show that the resonance scattering state belongs to the t2 representation of the Td point group, which is also the representation of the lowest unoccupied molecular orbital (LUMO) of GeH4. Energy loss spectra recorded in the electronic threshold region of GeH4 reveal enhanced inelastic scattering at large angles in the loss range 7-9 eV characteristic of excitation to the lowest triplet state.