How to extract lines between tags into different files?

I have an xml file with the below data:

 
unix>Cat  address.xml
<Address City=�Amsterdam� 
Street = �station straat�
 ZIPCODE="2516 CK   " 
</Address>
<Address City=�Amsterdam� 
Street = �Leeuwen straat�
 ZIPCODE="2517 AB " 
</Address>
<Address City=�The Hauge� 
Street = �kirk straat�
 ZIPCODE="2273 VP " 
</Address>
<Address City=�The Hauge� 
Street = �grotemarkat�
 ZIPCODE="2331 VZ " 
</Address>

I would like to extract each Address into a temparory file, that means for above data I need to extract block of data between <Adress> and </Adress> into some temp1, temp2, temp3 and temp4.

Any suggestion, how to do this using perl or awk?

Thank you very much

awk '/<Address/{i++}{print > "temp"i}' address.xml