We study the transmission, reflection, and absorption of ultralow frequency waves at density nonuniformities in low beta plasmas, such as plasma structures in the solar corona, inhomogeneities in the solar wind, and, at times, in the magnetopause. We simulate the time-dependent interaction of a monochromatic magnetohydrodynamic (MHD) wave with a planar plasma transition layer aligned with the magnetic field. When the incident wave front reaches the initially unperturbed transition layer, a resonant sheet starts to develop within a thin layer where the conditions for resonant MHD wave mode conversion are satisfied. In this sheet the wave amplitude is found to grow exponentially until a saturation level is reached due to dissipative effects. Dissipation controls the thickness of the sheet, the saturation level, and the time needed to reach the saturation regime. The resonantly absorbed energy, however, is essentially independent of the dissipation coefficient. The simulations are carried out in the context of linear resistive low beta magnetohydrodynamics. The simulation results are important for the case of the magnetopause as the enhanced wave amplitudes found inside the transition could promote diffusive mass transport across the layer.