Laser desorption of deuterium implanted in hot-pressed silicon carbide samples was performed. The samples had been implanted at ion energies ranging from 1 keV/D to 3 keV/D and at fluences from 0.6x10(20) m(-2) to 1.8X10(21) m(-2). For the high fluence samples (greater than or equal to 3X10(20) m(-2)), comparison of the experimental data of desorption rate versus laser energy with the results of computer simulations reveals that second order detrapping is the limiting re-emission process. The effective trap activation energy decreases from 0.9+/-0.1 eV/molecule at 1 keV/D to 0.5+/-0.1 eV/molecule at 3 keV/D. Blister formation and exfoliation or other forms of radiation damage could explain the energy dependence in the high fluence samples. At low fluence (<3X10(20) m(-2)), most of the D-2 re-emission takes place above the melting threshold (12 kJ/m(2)). Computer simulations, using the thermal properties of the solid phase of SiC extrapolated above the melting point, give information about the nature of the detrapping process. A first order detrapping mechanism with an activation energy of 2.0+/-0.2 eV was found under those conditions. A comparaison is made with the deuterium laser desorption behaviour in Be, C and Si.