ASHKELON, Israel — In southern Israeli towns and cities, anxiety from the casualties inflicted by missiles from Gaza are mixed with satisfaction that Israel's military is trying to settle the score with their militant tormentors.

Four Israelis were killed, including a soldier, and two seriously wounded Monday in rocket barrages, some deeper into Israel than ever before. A woman was killed when a missile crashed into a bus stop in the city of Ashdod, 23 miles from Gaza, the farthest Hamas militants have fired to date. Another woman was killed in a village next to Gaza.

Ashkelon, a city of 120,000 11 miles north of Gaza, suffered its first rocket death when an Israeli Arab worker was killed at a construction site. Overall, five Israelis have been killed in rocket attacks since the Israeli offensive began Saturday.

Deeper in Israel people are increasingly fearful, and many are following army instructions to begin preparing bomb shelters.

After the first Hamas rockets hit Monday in Ashdod, a port city of 190,000, the military extended its rocket warning system to include Beersheba, the largest city in southern Israel. Residents were instructed to prepare shelters and practice emergency measures.

Beersheba looked normal on Monday, with streets, bus stations and malls alive with people. But the new threat was certainly on people's minds. The front page of a local newspaper, "24 Minutes," blared with the headline: "Opening the shelters."

Ortal Levy, a 30-year-old mother of two, said she had never even entertained the notion that her bustling city could be within rocket range. Now she was preparing her bomb shelter.

"It's scary. We hope we are not dragged into this group of communities," she said, referring to the towns already under rocket fire.

Outside the central bus station, Mazal Ivgi, 62, was reading up on the latest in the newspaper.

"In the meantime, it's hard to believe that we could get hit," she said. "But when the first 'boom' comes, we'll also have to get used to a new situation."

In the working-class border town of Sderot, which has been targeted by relentless Gaza rocket salvoes, residents were pleased with the waves of Israeli airstrikes against Hamas positions in Gaza.

"It's about time," said Victor Turjeman, a 33-year-old electrician. "We've been waiting for this for eight years."

Sderot has been pounded with several thousand projectiles since 2001. The rockets have killed eight, injured hundreds more and made daily life unbearable.

Turjeman said his four children have been traumatized by the near daily attacks, his home has been damaged and his brother had a heart attack after a rocket exploded nearby. He fears escalation, but said he was pleased Hamas was finally being punished.

"We should keep pounding them until they beg for mercy," Turjeman said. "As far as I'm concerned, all of Gaza can be erased."

Unlike the new targets, the residents of Sderot are well versed with life under fire. Sderot Mayor David Buskila said his 24,000 citizens were still scared, but mostly overjoyed that something was being done to alleviate their suffering.

"We felt abandoned for so long, that our despair was ignored. We felt like we weren't even a part of Israel," he said. "Now we feel like the army is actively protecting us."

Israel Katz, a social psychologist at Hebrew University in Jerusalem, said the reaction in Sderot was a natural one.

"Fear and rage are often intertwined," he said. "These are people who feel vulnerable and all of a sudden they feel empowered. It's the same kind of satisfaction that a child who has been picked on gets when he hits back."

In Ashkelon, the reality Sderot has faced for years was beginning to sink in after Monday's missile crashed into a construction site, killing one worker and wounding several others.

Looking at the damaged site later in the day, Yitzhak Daboosh shook his head in disbelief. The 58-year-old father of two has spent his entire life in Ashkelon, and said he now fears for the safety of his family.

"These missiles have no address. Only God is watching over us now," he said. "We've been through a lot of things here, a lot of wars. But something like this? Never."