The illegal manipulation of affairs to avoid (or evade) paying tax that is due under the laws of a particular country. This is different to tax avoidance which is the perfectly legal activity of operating inside the rules and regulations and paying what is due.
What finally got Al Capone sent to prison, so you know that it is illegal! Not paying what is due, or deliberately manipulating affairs against the laws of a country is Tax evasion and therefore illegal. Tax avoidance is legal, and is making best use of the rules.