I think what @blr_p is referring to is Flash messages. It is "ON" by default in new sim cards and not everyone knows how to deactivate it.
For Lumia,
Go to settings -> mobile+SIM - > SIM settings -> SIM applications -> FLASH! -> Deactivate*
*Not sure what you will get to see after "FLASH!" because I have it deactivated since a long time. Basically you just need to deactivate Flash messages.
I have not seen the option for "WAP push messages" in Windows Phone OS.
For Lumia,
Go to settings -> mobile+SIM - > SIM settings -> SIM applications -> FLASH! -> Deactivate*
*Not sure what you will get to see after "FLASH!" because I have it deactivated since a long time. Basically you just need to deactivate Flash messages.
I have not seen the option for "WAP push messages" in Windows Phone OS.