NGOs and political parties have started a relief effort with the help of volunteers and donations in an attempt to help the refugees, many of whom have abandoned their homes with no money or belongings.
Schools and other public buildings across the country have opened their doors to refugees. There are an estimated 60,000 people seeking refuge in Beirut alone.
Ghassan Makarem, an NGO worker, said: "There's a big group of us co-ordinating relief work, because the government did not think of this. Yesterday we had 40 schools and around 500 persons in each school, but today I think that number has doubled or tripled.
"We were finding them everywhere. There were people hiding in half-built buildings, on the beach, if you go to any space in west Beirut you will see people staying there, sometimes in parking lots."
Those involved with the operation say the Lebanese government has provided little support, and facilities for refugees in Beirut are already overstretched.
"Most of the schools are now full. They are sending them to other areas of Lebanon," said one volunteer, who declined to give his name.
Volunteers said there was space in schools in the north of the country, but there was no transport available to move refugees there.
Many left behind
NGOs expect the number of refugees to rise as the conflict worsens. On Sunday, at least 20 Lebanese were killed in Israeli attacks, including 16 in a strike on Tyre, a large town in the south.
One man staying in a school in Ashrafieh in east Beirut, who had fled his village near Tyre, said most of his family had been unable to leave after the roads were destroyed.
NGOs say the number of refugees
will go up as the conflict worsens
"My wife and two daughters can't get out. My brothers and cousins are also there. In the area where I am from they are bombing heavily and they hit the local hospital," he said.
Although many have fled the south, tens of thousands remain in areas close to the border with Israel.
"Most of the villagers are still there and there are many women and children," the man said.
Another man in the school had fled the southern suburbs of Beirut with his family and said only a handful of people remained in the area that has been bombed heavily for the last three days.
"We ask the West to help us and stop the bombing and let us return to our homes. The women and children are in a state of panic," he said.