buy back of shares

This is the case of listed company shares. So, the difference between consideration received and cost of acquisition is taxable as capital gain. In case shares are held for long term, indexation facility is available.
But,if it will be in case of unlisted shares, the company has to pay additional income tax @ 20percent(plus surcharge and education cess). It will be exempt in the hands of shareholders.

prudhvi sir will you explain with the help of an example please

If shares are held for long term , then capital gain will be exempted or not under section 10(38).

We can't claim exemption of sec 10(38),because buyback is different from transfer of shares. In transfer, shares will exist but in buyback they will cease to exist. So, taxability arises.