A rotary cutting machine 10, if inclined at large angles, provides positive supply of a cutting oil and avoids leakage of the cutting oil. The machine 10 has a machine body 14 and an arbor 18. An oil tank 50 is mountable to the machine body 14 so that the oil tank 50 is oriented at a given angular position about the central axis of the arbor 18. The tank body 54 has an interior space. The interior space is divided into a first interior part and a second interior part by an imaginary plane containing the central axis of rotation of the arbor. The first interior part is less in volume than the second interior part.