|The development of free-electron lasers and new generation light sources is enabling therealisation of high intensities and short pulse durations exceeding the currently attain-able∼1023W cm−2 and atto second time scale limits. These extreme laser limits should make it possible to unravel new science which is not yet feasible at the current laser parameter regimes. The very high intensity of radiation sources and the short pulse duration is anticipated to enhance imaging of tiny structures with very high resolution,filming of ultra-fast processes, and studying matter under extreme conditions. Besides the new frontiers likely to be unfolded, significant challenges exist in the theoretical simulation of these non-linear processes. In the weak-field intensity regime, the electric dipole approximation has been quite successful in describing the light-matter interac-tion dynamics reproducing many of the experimentally observed features. But at theunprecedented intensities and x-ray wavelengths produced by the new light sources, the electric dipole approximation is likely to break down. The role of higher multipole-order terms in the interaction Hamiltonian, associated with the radiation pressure, is then expected to become important in the accurate description of the interaction dynamics.This study extends the solution of the non-relativistic time dependent Schrödinger equation for a single active electron system interacting with short intense laser pulses beyond the standard dipole approximation. This is realized using both the Taylor and the Rayleigh plane-wave multipole expansion series of the spatial retardation term. The inclusion of higher multipole-order terms of the interaction is expected to increase the validity and accuracy of the calculated observables relative to the experimental measurements. In addition, it is shown that for equivalent laser parameters the Rayleigh multipole expansion series is more accurate and efficient in numerical convergence. The investigated non-dipole effects manifest in both differential and total ionization probabilities in form of the increased ion yields, the distorted above-threshold-ionization structure, and asymmetry of the photoelectron angular distribution in both polarization and propagation directions. The non-dipole effects are seen to increase with intensity, wavelength, and pulse duration. The results for hydrogen as well as helium atom are presented in this study. A new model potential for helium, and any other two-electron atomic system, yielding reasonably accurate results within the frozen core approximationis also developed.