The acoustic radiation force resulting from a 2D focused Gaussian beam incident on a cylindrical object in an inviscid fluid is investigated analytically. The incident and the reflected sound fields are expressed in terms of cylindrical wave functions and a weighting parameter, describing the beam shape and its location relative to the particle. Our main interest here is to study the possibility of using Gaussian beams for axial and lateral handling of rigid cylindrical particles by exerting attractive forces, towards the beam source and axis, respectively. Results have been presented for Gaussian beams with different waist sizes and wavelengths and it has been shown that the interaction of a focused Gaussian beam with a rigid cylinder can result in attractive axial and lateral forces under specific operational conditions. Results have also revealed that attractive axial forces generally occur when the backscattering amplitude is suppressed. The results provided here may provide a theoretical basis for development of single-beam acoustic handling devices.