Based on the asymptotic diffraction theory methods, the problem of determining the near field of the convex cylindrical antenna array composed of aperture radiators is reduced to the boundary value problem in the single cell of the array, which is solved using the Galerkin method. The asymptotic theory is further developed, which provides representation of the radiator diagram in the convex cylindrical array as a sum of the direct wave from the excited radiator, the fast creeping waves and slow creeping waves. Results of numeric computations of the slot elliptical, particularly circular antenna arrays are presented.