The Chilean miners trapped in a collapsed mine shaft are starting to rebel against restrictions imposed by their government as they enter their second month below ground.

Family members said the 33 men had protested that the government was censoring letters and restricting information to them during a video conference at the weekend.

The miners have also shown increasing independence in recent days as they rejected one food delivery of peaches and continued to drive vehicles around the mine tunnels 700m below ground, disregarding explicit orders not to do so. They are also increasingly vehement in their demands for wine and cigarettes.

Family members said the miners were angry because they had not received much mail. "He totally cursed me out, they are not sending the letters to him," said the son of trapped miner Victor Zamora. "He is going to blow up down there."

"It is a big problem that they are not getting the letters," said the nephew of miner José Ojeda. "They are very angry."

Luis Urzua, the leader of the miners, on Saturday told rescue officials that failure to deliver the letters was a major item of discontent among the trapped men.

Government officials at the rescue site have repeatedly explained to family members that only letters with positive messages will be delivered. But rescue officials also promised to streamline the postal service and create a central log for letters sent and letters received.

"They say they are not sick," said one rescue leader, who asked not to be named. "They want to go back to their regular life. This is what we have been hearing over and over again from Nasa."

Nasa officials who have gone to Chile to help support the trapped men said their behaviour was not unusual. Briefing the rescue leaders at the weekend, Nasa consultants said that during one space mission, the astronauts simply refused to speak to Mission Control and switched the communications system off.

"This [anger and stress] is common in groups under isolation. They [the miners] have nowhere to go for support," said Professor Nick Kanas, professor of psychiatry at the University of California, San Francisco, and long time consultant to Nasa. "After six weeks the situation turns sterile and confining. What was once quirky and fun – like the jokes of a colleague – become irritable and tiresome."

Despite the concerns about censorship of written communications, many families were elated at the new video system. "You saw daddy, you saw daddy," said Veronica Quispe, 20, wife of Bolivian miner Carlos Mamani, the only non-Chilean among the trapped men. With her one year old daughter Yemily, who was breastfeeding, Quispe danced around the rocky mountainside.

Carolina Lobos, 26, daughter of Franklin Lobos, the football star cum miner trapped in the San José mine, said her father was looking very well. "We told him that when he gets out, we are going to have a huge party, a blowout!" she said. "He looks great." She thanked the technicians for installing the fiber optic video connection: "It was like he was in the living room, right here."

Her sister Claudia Lobos, 20, said: "I tried to be strong, but I cried at once. We were so excited we didn't let him talk."