The method of current and charge integral equations  is applied to numerical electrodynamic analysis of radiation and impedance matching characteristics of parabolic antennas with reflector diameter from 0.5 to 10λ. As a result as opposed to the current method relying on physical optics approximation the influence of feed on reflector’s radiation pattern, the influence of reflector on feed’s impedance matching and the contribution of feed’s rear radiation into reflector’s radiation pattern are all accounted for. A new model of representing a parabolic surface in the form of its square approximation is suggested, which provides almost uniform partitioning grid and has at least 2.5 times less boundary elements that the common revolution surface representation while having the same sampling coefficient. Dependences of antenna’s directivity on reflector dimensions (0.5–10λ) are calculated for six different focus distance to reflector’s diameter ratios using the developed by the authors crystal_U software package. The calculated results are confirmed by good matching with well-known experimental results.