The energy absorption mechanism in the close near field of dipole antennas is studied by numerical simulations. All computations are performed and validated applying the three-dimensional multiple multipole software package. The numerical model of the plane phantom is additionally checked by accurate as possible experimental measurements. For the plane phantom, the interaction mechanism can be described well by H-field induced surface currents. The spatial peak specific absorption rate can be approximated within 3 dB by a formula given here based on the incident H-field or antenna current and on the conductivity and permittivity of the tissue. These findings can be generalized to heterogeneous tissues and larger biological bodies of arbitrary shape for frequencies above 300 MHz. The specific absorption rate is mainly proportional to the square of the incident H-field, which implies that in the close near field, the spatial peak specific absorption rate is related to the antenna current and not to the input power.