The influence of surface excitations on electrons elastically backscattered from solid surfaces is investigated. Elastic-scattering differential cross sections are calculated using the partial-wave expansion method and the finite difference techique for solid atoms with the Hartree-Fock-Wigner-Seitz potential. An extended Drude dielectric function which allows the characteristic oscillator strength, damping constant, and critical-point energy for each subband of valence electrons is employed to estimate electron inelastic mean free paths for volume excitations. The same dielectric function is applied to evaluate the probability of surface excitations for incident and escape electrons by including the recoil effect without the small-angle approximation. Results of Monte Carlo simulations on the elastic reflection coefficient and the angular distribution of electrons elastically backscattered from Cu and Ag surfaces are presented. It is revealed that surface excitations significantly reduce the elastic reflection coefficient for low-energy electrons, but less significantly influence the angular distribution for large escape angles. Our results agree very well with experimental data.