In this article we give a sufficient and necessary condition to determine whether or not an element of the free group induces a non-trivial element of the free Burnside group of sufficiently large odd exponent. Although this result is “well-known” from the specialists, it has never been stated with such a level of simplicity. Moreover our proof enlighten some important differences between the Delzant-Gromov approach to the Burnside problems and other existing ones. This criterion can be stated without any knowledge about Burnside groups, in particular about the proof of its infiniteness. Therefore it also provides a useful tool to study outer automorphisms of Burnside groups. In addition we state an analogue result for periodic quotients of torsion-free hyperbolic groups.