PURPOSE: To improve closely attaching air-tightness, by forming splits in tooth crests in meshing parts of rotors in a positive displacement rotary pump.

CONSTITUTION: Two rotors 1, 2 of a Root's pump, which rotate while they are meshed and brought into contact with each other in their external surfaces, are slided coming into contact with an outer casing 3. Splits 1a, 2a are respectively formed in tooth crests of each rotor 1, 2. Accordingly, the pump, forming elastic construction of laterally extending and contracting corresponding parts interposing the split groove, enables air-tightness of a contact surface to be held to a high degree by elastically spreading point end parts corresponding to the contact surface wide and narrowly changing, and pump action can be improved.