Photolithography is used to fabricate an annular slit on an elastomeric substrate. The shape of the aperture is altered through the application of unidirectional mechanical strain. With an unmodified annular slit, standard Bessel beams with circular intensity distributions are obtained over a propagation distance of 20–50 cm. By simply stretching the same elastomeric optical element along one axis, elliptical Bessel beams are generated over a similar propagation range. Non-diffraction and self-healing are exhibited by Bessel beams formed with an elongated annular slit. Experimental results for intensity profiles are consistent with a treatment of Bessel beams as Fourier transforms of circular apertures.