A perturbational procedure for reducing sidelobe level and increasing resolution of antenna arrays with uniform amplitude excitation by introducing random element displacement with respect to the periodic configuration is presented. The element displacement is considered as a random variable subject to a certain probability distribution function (pdf). The simulated beampattern of the random array is obtained by ensemble averaging of many realizations of element displacement. For comparison, the beampattern is evaluated by using uniform and Gaussian pdfs. In the case of Gaussian distribution, it is found that the peak sidelobe can reach very low levels with increasing the number of elements, whereas it is almost fixed around − 30 dB in the case of perturbation by uniform distribution function. Moreover, as the number of elements increases, Gaussian distribution shows better beampattern with less number of sidelobes compared to the uniform distribution. This result is consistent with random array theory. In either distribution, and for a fixed number of elements, lower sidelobe levels and less beamwidths are obtained, in contrast with amplitude tapering techniques.