This paper presents an analysis of the dose rate in tissue irradiated by an electromagnetic near field of a circular loop antenna. An analytical model comprised of a circular loop antenna located in the vicinity of the semi-infinite plane of a homogeneous biological medium was formulated. A quasi-static hypothesis was not introduced. The theoretical formulation was rigorously developed based on Maxwell equations which used an electric vector potential, cylindrical coordinates and a Hankel transform. The internal electric field E and the specific absorption rate (SAR) were adopted as indices for the dose in the tissue. This formulation was applied to the dosimetry of a high-frequency therapeutic device (HFTD) and experiment of irradiation to a frog web. The frequency of the applied electro-magnetic fields (EMF) was 9-10MHz. The distance between the antenna and tissue was 2.0-3.2mm. The dose of HFTD were 0.75V/m and 0.35mW/kg, respectively. The dose of experiment of the irradiation to a frog web were 0.42-2.08V/m and 0.11-2.69mW/kg, respectively. The SAR values obtained by this analysis were small enough to conclude that the effects were non-thermal. The calculated SARs of these experiments were compared with estimated SARs in experiments on calcium efflux change due to a weak modulated RF field. All were found to be of the same order of magnitude.