Results ofdesign and investigations of elliptically polarized millimeter wave antenna arrays are shown. A presented leaky-wave antenna arrays consist of the waveguide structure and finite diffraction grating. The diffraction grating is excited by E type surface wave, which is the eigen wave of the waveguide structure. The difraction grating consist of rectilinear and parallel nonhomogeneities, which are disposed at an angle of a in the direction of surface wave propagation. The angle a widths and distances between nonhomogeneities are choosing by using special optimization algorithms in order to receive necessary electrodynamics characteristics.