is it possible to set camp at an israeli beach for a few days ? for free?

it depends on where u want to camp israel has a huge shoreline in comparison to its size so if youll go to an unoficial beach there should be no problem campin' for free
those could be found anywhere north and south from main coast cities i specially like gaash beach and apolonia beach both not far from tel aviv

There is a possibility to camp for a few days in several places along the coastline.
at the free camping section the mail rule is : you get what you pay , meaning ,no facilities or limited access by vehicle , though some of these sites are extremely beautiful and not crowded
At the north :
-"Betzet" beach, northern to Naharia
"Hof Hacarmel"( the Carmel beach) near Haifa
-"Atlit" beach, a bit southern to Haifa.
-"Habonim" beach ,southern to Haifa .( only at the northern part, and without vehicle )
Center:
-"Yannai" beach , north to Natania , low cost camping with facilities
Most of the Tel Aviv area is forbidden for camping
South:
-"Nitzanim" beach , south to Ashdod (payment only in the summer), with facilities.
There are more , but these are the main ones .

Note: please check in advance that the area that you plan on camping in is not prohibited for camping , otherwise you can get fined.