In this study, the light propagation in a structure consisting of SiOx on Si substrate with Al nanoparticles regularly placed in the SiOx layer is considered. Numerical modelling is performed by solving the Maxwell equations for the electromagnetic waves. In distinction from the well-known finite-difference time-domain (FDTD) simulation technique, we do not solve time-dependent wave equations here; rather, we propose a new numerical technique. This technique allows us to determine the stationary amplitudes of the electromagnetic oscillations directly from the linear algebraic equation system. The obtained results apply to silicon solar cells with an SiOx + Al top layer to maximise their efficiency. We found that 26 nm and 39 nm diameters of spherical Al nanoparticles are nearly optimal for a λ = 435.8 nm wavelength of the incident light. In addition, we evaluated the (nearly) optimal parameters of their placement in the SiOx layer. The results show the possibility of increasing the efficiency of solar cells by increasing the light absorption inside the active Si layer from ≈60% to ≈80%. Future perspectives on the proposed method and its possible applications are discussed.