A machine and a method for the laser working of profiles (P) are described, in particular for carrying out an inclined cutting operation on the profile (P), for example for making a flared hole (H), wherein before the working operation a support and guide device (12) is positioned in a given starting position along the longitudinal axis (x) of the profile (P) with respect to a working head (10), and then, during the working operation the support and guide device (12) is moved along the longitudinal axis (x) integrally with a feeding device (14), i.e. integrally with the profile (P), so as to keep constant, during the working operation, the extent of the projection (A) of the profile (P) from the support and guide device (12), said integral movement of the support and guide device (12) with the feeding device (14) being limited to that portion of the movement of the feeding device (14) which is required to compensate for tilting movements of the working head (10) about said axis of oscillation (t).
