A continuous mining method includes operating a vibratory milling machine having a milling head, a base, and a milling tool to oscillate the milling head in a substantially linear reciprocating fashion relative to the base to move the milling tool along a milling axis; and advancing the vibratory milling machine in a work piece in a cutting direction and wherein milling axis is oriented at an attack angle relative to the cutting direction, the attack angle being between about 0 and about 40 degrees.