A wet wire drawing machine (1a, 1b) particularly for drawing very high strength steel wires, comprising: - a station for unwinding a coil of crude wire from a rotating spool, - a plurality of intermediate drawing stations (4, 5, 6) which are arranged sequentially with respect to each other and are provided with means for the lubrication of at least the drawplates with which they are provided, - a final wire drawing station which is provided with wire straightening means so as to obtain a processed wire having the desired geometric shape and mechanical characteristics, - a coil winder arranged in output with respect to said final wire drawing station for winding said processed wire into a coil, the wet wire drawing machine (1a, 1b) being characterized in that it further comprises: - anti-slip pulling means which are associated with the last one of said intermediate wire drawing stations so as to eliminate irregularities in the wire processed in said intermediate wire drawing stations (4, 5, 6) and attenuate the vibrations of the rotating elements of said intermediate wire drawing stations (4, 5, 6), each one of said intermediate wire drawing stations (4, 5, 6) comprising at least one drawplate which is interposed between a guiding cone and a traction cone whose rotation axes (9a, 10a) are parallel and mutually side-by-side, each one of said traction cones and each one of said guiding cones comprising respectively a plurality of traction tracks and a plurality of guiding grooves which are mated in pairs and are provided on progressively increasing diameters so as to have a geometric consistency between the length of the path followed by said wire being processed and the length of said wire being processed that increases at each pass in said at least one drawplate in compliance with the limit of elasticity of the material of which said wire being processed is made, said wire being processed being wound alternately and partially on said cones (9, 10), passing from one of said traction tracks to the next by means of a respective one of said guiding grooves through said at least one drawplate, so as to pass, along the advancement direction of said wire being processed, from the smaller diameters of said cones (9, 10) to the larger diameters of said cones (9, 10), said anti-slip pulling means comprising a first pulling flywheel, which is external to said intermediate drawing stations (4, 5, 6) with an independent motor drive and in use takes said processed wire from the last one of said traction cones with synchronization by means of a second synchronizing dandy pulley with adjustable countertraction, adapted to eliminate the slippages between said first pulling flywheel and said last traction cone, and said anti-slip pulling means comprising an idler disk, which is associated rotatably and axially with said last traction cone about the rotation axis of said last traction cone and has an outside diameter that is equal to the diameter of the last traction track of said last traction cone, said processed wire that exits from said last traction track arriving at said first pulling flywheel by passing first through said second synchronization dandy pulley and then through said idler disk, said final wire drawing station being provided between said idler disk and said first pulling flywheel. - a station for unwinding a coil of crude wire from a rotating spool, - a plurality of intermediate drawing stations (4, 5, 6) which are arranged sequentially with respect to each other and are provided with means for the lubrication of at least the drawplates with which they are provided, - a final wire drawing station which is provided with wire straightening means so as to obtain a processed wire having the desired geometric shape and mechanical characteristics, - a coil winder arranged in output with respect to said final wire drawing station for winding said processed wire into a coil, - anti-slip pulling means which are associated with the last one of said intermediate wire drawing stations so as to eliminate irregularities in the wire processed in said intermediate wire drawing stations (4, 5, 6) and attenuate the vibrations of the rotating elements of said intermediate wire drawing stations (4, 5, 6),