We investigate nonlinear diffraction (NLD) of laser radiation in circularly poled nonlinear quadratic crystal for the case of single and two fundamental pump beams. We show that single pump beam excitation (10 ps @ 1.053 μm) along Z axis of circularly poled structure (with period 7.5 μm) leads to the second harmonic signal being emitted in a form of multiple low order cones (rings) and one strong external SH cone (ring) defined by the longitudinal phase matching conditions. We study a dependence of the NLD pattern as a function of the incidence angle of the pump. We demonstrate that two noncollinear pump beams intersecting exactly in the center of the structure results in a new type nonlinear diffraction, which does not have an analogue in linear optics. It features a set of nonlinearly diffracted beams originating from each individual pump accompanied by the set of additional diffraction rings which originate from photons coming from both pumps. The corresponding phase matching conditions responsible for the observed NLD effects are discussed. The observed effects represent nonlinear generalization of optical diffraction in linear media and we believe can find possible applications in second harmonic optical microscopy.