Wave motion is only possible in the medium which possess the property of elasticity and inertia how?

First off
It;s mechanical wave motion for which elasticity and inertia are necessary, electromagnatic waves can travel even without a medium

Elasticity is necessary as for mechanical wave to propogate there needs to be some kind of vibration of the moecules of the medium and hence they need to be elastic

wave is essential transfer of energy so it usually fluctuates between potential and kinetic energy, and for kinetic energy to exists inertia is necessary