The electrochemical insertion of sodium ions into different types of hard carbons was achieved in electrolytes composed of ethylene carbonate as the solvent and NaClO4 as the salt. For all the materials studied the sodium uptake increases when the carbon highest heat treatment temperature (HTT) decreases. PAN-based carbon fibres appear to be suitable structures to allow significant sodium insertion. Thus, T650 ex-PAN fibres lead to a reversible capacity close to 209 mAh g(-1). In that case, sodium insertion occurs in two main ways: one is the adsorption on the single graphene layers and the other is the concomitant insertion into the porosity that occurs below 0.1 V versus Na+/Na. This second mechanism, which is indicated by a low-voltage plateau on the electrochemical curves, allows significant insertion. The compared electrochemical study of two saccharose-coke samples corresponding to different regions of Dahn's classification underlines the importance of the carbon precursor and of the manufacture process. The reversible capacity is equal to 184 mAh g-1 for the sample heat treated at 800 C which presents a high hydrogen content whereas it is close to 145 mAh g(-1) for the one characterized by a HTT of about 1500 C and a low hydrogen content. The best electrochemical performances are obtained for pyrolyzed cellulose carbons. Indeed, the reversible capacity is about 279 mAh g(-1). Outgassing these carbons at 950 degreesC results in such a decrease of the reversible capacity down to 145 mAh g(-1). That can be related either to the thermal elimination of heteroelements or to modifications of the pore size distribution. Consequently, the most suitable hard carbon material for anodic applications in rechargeable sodium-ion batteries should both present a high residual hydrogen content and a significant microporosity.