Abstract: It is described respectively in detail how the concepts of inertia and inertial mass are introduced in both the Newtonian mechanics and the special relativity.The proper（or rest） mass of a particle has been shown clearly that it is exactly equal to its inertial mass in the special relativity as in the Newtonian mechanics.Through analysis,it is pointed out and emphasized that the relative（or moving） mass is only a prescription but not a results due to that the inertial mass of moving particle has changed really.Finally,the specific property that the particles with zero rest mass and with light speed comply with special relativity but not comply with Newtonian mechanics is explained.

Key words: Newtonian mechanics, special relativity, inertia, inertial mass