We describe the collisions of an electron with a target atom in the presence of a strong, linearly polarized, monochromatic, oscillating electric field in the Kramers-Henneberger gauge. We show that the resulting set of coupled-channel equations, originally derived by Gavrila and Kaminski [Phys. Rev. Lett. 52, 613 (1984)], represents electron scattering by a vibrating charge initially in a highly excited state. This formulation leads to a mechanical model of the atom-field interaction from which we can draw better insights into the nature of the process. We solve these coupled equations numerically in the close-coupling approximation by a combination of the linear algebraic and R-matrix propagator approaches. We specifically treat electron-proton collisions in an intense field and investigate the capture-escape resonances over a range of intensities and frequencies. We also investigate multiphoton ionization of atomic hydrogen in various intensity regimes. We extend our calculations for single-photon ionization into the superintense regime ( > 10(16) W/cm2) and compare our results with results from time-dependent solutions of the Schrodinger equation.