Abstract: The invention relates to a cutting machine for cutting a flexible material by a cutting wheel rotated by a motor. The cutting wheel and the motor are carried by a cutting head mounted to move horizontally along two orthogonal axes and to rotate about a vertical tangential servo-control axis. The invention further includes a support table covered with a mat into which the cutting wheel penetrates. The cutting wheel is adjustable to change the depth to which the cutting wheel penetrates into the mat. The cutting wheel is also adjustable to change the horizontal distance between the vertical tangential servo-control axis and the axis rotation of the cutting wheel so that the cutting wheel penetrates into the mat a front contact point situated in the vicinity of the tangential servo-control axis.