We discuss the Gaussian beam mode analysis of Bessel beams, eigen-solutions of the wave-equation in cylindrical polar coordinates which neither change form nor spread out as they propagate. Approximate, limited diffraction finite aperture, pseudo-Bessel beams having intense on-axis spots with large depths of field can be produced experimentally in the far infrared by using plastic conical lenses, known as axicons. We illustrate the physical insight provided by Gaussian beam mode analysis of such systems. Such pseudo-Bessel beams can be usefully approximated by high-order Gaussian–Laguerre modes, which have similar propagation characteristics. The size of the on-axis spot produced by an axicon, and its depth of focus, can be estimated from a single best-fit high-order Gaussian–Laguerre mode, and a more detailed description of behaviour can be achieved by adding a few additional modes of neighbouring orders. The strength of Gaussian beam mode analysis is that it is straightforward to model the propagation of Bessel beams through complex systems of long wavelength optical components, such as apertures, mirrors, and lenses. We report the experimental generation and measurement of a 0.1 THz Bessel beam, and show that useful performance is possible for an axicon having a scale size just one order of magnitude greater than the wavelength. This work confirms the technical feasibility of designing and building long-wavelength optical systems based on Bessel beams.