A method for assessing ionising radiation doses from laser plasma sources is presented. Results of an example used to demonstrate the method indicate that, under the assumptions of the analysis, the directional dose equivalent at 0.07 mm depth (H'(0.07)) for photon energies E_p greater than or equal to 10 keV is 75 mu Sv J^-1 of laser energy, assessed at 1 m (dry air) from a plasma source. The highest component of this dose equivalent ( approximately 12 mu Sv J^-1 keV^-1) results from photons of energy around 10 keV. For the same example, the directional dose equivalent at 10 mm depth (H'(10)) for E_p>or=10 keV is 20 mu Sv J^-1; the highest component of which ( approximately 1.3 mu Sv J^-1) resulting from photons of energy between 15 and 20 keV. Further examples given in this study predict the reduction in the dose equivalents when additional attenuating media are used between the source and an exposed person.