We have calculated (using a simple theory) the paramagnetic-resonance absorption by conduction electrons in a thin metallic sample, thus extending the earlier work of Dyson. Our results are for a metal sample of arbitrary thickness, with a static magnetic field ${\mathcal{H}}_{0}$ at arbitrary angle with respect to the sample surface, and under either classical or anomalous skin-effect conditions. The electromagnetic field is assumed to be incident normally on both sides of the sample, but the relative phase and/or amplitude on the two sides can be arbitrary (asymmetric excitations). Under anomalous skin-effect conditions, as the field ${\mathcal{H}}_{0}$ is rotated from parallel to normal, the shape of the spin-resonance line is modified. For asymmetric boundary conditions on the electromagnetic field, the line decreases in intensity (to zero under certain conditions). For a symmetric excitation, or when the electromagnetic field is incident on one side only, the line shows a slight decrease in intensity and a slight narrowing as the field is rotated. Numerical results are presented.