- Israel has told civilians near the border to stay in shelters. But in Kibbutz Be'eri, residents said Palestinian militants were trying to get into homes and shelters.
- "The terrorists are trying to break into my house," Ayelet Hachim told Channel 12, Israel attack: People hide in homes from her home in the town of Kibbutz Be'eri, close to the Gaza Strip.
- Israel attack: Hideout in homes as militants use Gaza route
For hours, people in Israel have been phoning into news stations saying they're trapped in their homes, after Palestinian militants entered their towns and villages in a huge surprise attack.
Many are in hiding, saying they can hear gunfire, while others can not find loved ones.
"The terrorists are trying to break into my house," Ayelet Hachim told Channel 12, from her home in the town of Kibbutz Be'eri, close to the Gaza strip.
"I hear their voices and they are banging on the door. I am with my two little children."
Israel has told civilians near the border to stay in shelters. But in Kibbutz Be'eri, residents said Palestinian militants were trying to get into homes and shelters.
One resident living in the town told Channel 12 that "there's shooting from across the town, I'm at home and I hear them outside my house. We're sitting quietly, the entire town is quiet so they won't come for us".
And 23-year-old resident Ella said she has heard that "the terrorists are in the shelter", adding: "I still hear bursts of gunfire."
All homes in Israel are required by law to have bomb shelters, and there are also bomb shelters in public places too.
It is one of the most serious escalations in the Israel-Palestinian conflict in years - with fighters from militant group Hamas crossing into Israel from Gaza at dawn, using motorbikes, paragliders and boats in an unprecedented assault.
They claim to have taken dozens of Israelis captive, while in the the town of Sderot, gunmen purportedly opened fire on residents.
At least 40 people have been killed in Israel, the country's emergency services say.
"I've been in the shelter with my week-old baby for over two hours, while my house is on fire," said one resident of Kibbutz Nirim, near to the Gaza strip, on Channel 13.
Other residents have been putting out pleas on social media.
"Urgent, urgent, please help this get to the media," Ella Mor wrote on Facebook. "We need to save my nephews who are in hiding. They called to say that they shot their mum and dad and they're dead in Kfar Aza. They can't find the baby girl.
"The police don't answer; Magen David Adom [Israel's emergency medical service] can't get to the Kibbutz."
'I have never been this frightened'
Elsewhere, a woman called Adele said on Facebook: "We have been told to lock doors, not leave the safe room. We're not even turning in the air-conditioning for fear it will signal a presence of people in the house.
"My stomach is turning. I hear a lot of shooting, even though the thick walls of the safe room. I need to go to the bathroom, but I dare not. I have literally never been this frightened."
In Kibbutz Nir Oz, in southern Israel close to the border with Gaza, a resident called Yoni wrote on Facebook: "They kidnapped my mother-in-law and left [with her] - I urgently need to get in contact with the army and media."
Ofir, a resident of Sufa, said: "We are locked in our shelter, the army isn't here. My husband is with the preparedness squad fighting outside. They're firing on us in our homes, trying to come into our houses.
"The Kibbutz WhatsApp group is going crazy with messages that people are writing that they're shooting on their houses. We are close to the fence, I don't know where the army is, there's no-one here."
The unprecedented attack by Hamas began early on Saturday morning, as the fighters used cover from a barrage of rockets.
The militants claimed to have fired thousands of rockets - with some targeting cities as far as Tel Aviv and Jerusalem.
English author and journalist Gideon Levy, who is in Tel Aviv, told the BBC: "The streets are totally empty. Restaurants, cafes everything is locked down and there is a heavy feeling of surprise, of shock and of fear from what is still expected to happen.
"When the first rockets fell, I was still jogging in the park, the noise was terrible."
Israel has launched waves of air strikes in the Gaza Strip in response.
Israeli Prime Minister Benjamin Netanyahu said Israel was "at war" and vowed that Hamas, Gaza's rulers, will "pay a price it has never known".
The strikes on Gaza have killed 161 and injured closed to 1,000 people, according to local Palestinian officials.