According to the latest rumor-mill, the ship dates for the Samsung Galaxy S4 in several Eastern European countries has been leaked and will commence in about two weeks. Here's a quote with some of the details,

According to the report, Russia and several Eastern European countries will see the 16GB 3G version of Samsung’s Galaxy S 4 begin shipping in mid-April and the LTE version will follow in late May. Then, the leak says the 64GB 3G and LTE versions of the phone will begin shipping in mid-June.
Sound off if you live in one of these areas, and for everyone else, stay tuned! We will bring you launch date details for other markets as they arrive.

Source: BGR