How are shell companies used for tax evasion? The recent release of leaked documents on Mossack Fonseca has information on corporations and individuals using the firm's services for, among other things, tax evasion:

The massive security breach shows how a global industry of law firms and big banks sells financial secrecy to politicians, fraudsters and drug traffickers as well as billionaires, celebrities and sports stars. [...]
Using complex shell company structures and trust accounts Mossack Fonseca services allow its clients to operate behind an often impenetrable wall of secrecy. Mossack Fonseca's success relies on a global network of accountants and prestigious banks that hire the law firm to manage the finances of their wealthy clients.
Panama Papers and Mossack Fonseca explained, Australian Broadcasting Corporation

What are &quot;shell companies&quot; and how can they be used to hide money or avoid paying taxes?
Another key feature of those shell companies is that they hide the ultimate beneficiary of the transactions. Banks, insurance companies and most financial services firm must make enquiries as part of the "Know Your Customer" (KYC) regulations: they should be able to find out who will benefit ultimately from the transactions, or in the name of whom they are carried out. THeoretically (ate least in the EU), if they fail to identify an ultimate beneficiary, they should refuse to carry out the transaction AND warn the responsible authority (typically the local equivalent or representative of the FATF - Financial Action Task Force)

But a succession of shell companies in different countries, in particular in countries which apply a strict confidentiality of the investors of a company, make it very hard to be sure that the beneficiary identified is indeed the ultimate beneficiary. 

Thus, those shell companies also serve the purpose to hide their owner to their counterparts. This feature is most appreciated for tax evasion and money laundering (obvisouly).