This paper deals with the electromagnetic field backscattered by a chiral object when illuminated by a linearly polarized plane wave. Computer simulations are carried out using four different computer codes, three of them based on a surface integral equation method using bidimensional finite elements for solving the scattering problem. The various shapes we consider are one- or three-turn regular helices, canonical helices, patterns appearing in pseudo-chiral or omega media, as well as non-chiral shapes such as wires and a loop studied for comparison purposes. They are mostly perfectly conducting, but the case of low and high permittivity dielectrics has also been treated. These objects can be embedded either in free-space or in a (lossy) dielectric medium. A first stage is devoted to the comparison of results given by the various computer codes for a three-turn regular helix and a canonical helix. For the latter, comparison with measurements will also be reported. Then, the far field responses of the various shapes are compared with one another for several incidences and polarizations of the incident field. The influence of the host medium and the nature of the target material are also mentioned for the particular case of a three-turn regular helix. Finally, we indicate how these results could be used in the field of chiral composites modeling.