After a general introduction on the main aspects of the mechanical properties of main-chain liquid-crystal elastomers (MCLCEs) and side-chain liquid-crystal elastomers (SCLCEs), new results will be presented dealing with several MCLCEs with a cross-linker density C = 8%, 6% and 4% and with a SCLCE with C = 10%, all prepared by the two-step cross-linking process. A non-SCLCE with bulky side-groups similar in shape to the mesogens was also synthesized for comparison with the SCLCE. Most of the experiments were performed with a piezorheometer allowing the determination of the shear anisotropy of the samples by applying shear in a direction parallel or perpendicular to the director, and with a thermo-elastic device for the E measurements. The main results concern: (a) the influence of the supercritical nature of SCLCE and the subcritical nature of MCLCEs on the mechanical properties of these elastomers, as well as that of SmC domains present in MCLCEs; (b) the relationship between the degrees of elongation and of anisotropy deduced from the variations of and during the poly-domain to mono-domain transition of the 10% SCLCE and the 8% MCLCE; (c) the determination of the Poisson's ratio showing that it is isotropic for the non-SCLCE, with a crossover between 0.5 (classical value for rubbers) for small strains and 0.38 for high strains, and anisotropic for the 10% SCLCE and 8% MCLCE, with values <0.5. The particular behaviors of the Poisson's ratios can be explained by confinement effects occurring when stretching increases.