Beside a storage platform, the machine mainly comprises a platform 40 on which there is offered up a roll 7 of turf which is pushed by a jack 45 onto an inclined plane, consisting of a belt 49, in line with which belt 49 there is positioned an unrolling belt 46 held by two lateral cheeks 54, which cheeks 54 hold a longitudinal component 61 by means of a free spindle 60.