President Reagan has cleaned house at the Environmental Protection Agency. Ten senior officials have resigned or been fired. William D. Ruckelshaus, his nominee to become the new administrator, announced last week that he has a "free hand" to restore the agency's strength and independence and to staff it with people of "iron integrity."

But the task before Ruckelshaus, who was the EPA's first administrator in 1970, is considerably larger than filling empty offices. It is the rebuilding of an institution.

The environmental agency bears deep scars from its first two years under the stewardship of Reagan's appointees, according to officials who ran the agency's programs under Republicans and Democrats in the past.

These officials say it has been hobbled by two years of deep budget cuts, administration resistance to regulation, a relaxation of enforcement efforts, elimination of research activities that provided the basis for regulation, plunging staff morale and an exodus of career professionals.

While the nomination of Ruckelshaus, who enjoyed support from both industry groups and environmentalists in his first tour of duty at EPA, has gone far to revive the morale of the agency staff, these officials contend the larger problems will not be solved so easily.

Anne M. Burford, the departed EPA administrator, "wasn't rejected by the American public because she had friends who owned polluting industries," said a congressional aide who helped write several major environmental laws. "That was why we were able to smile as we pushed her over the cliff. She was pushed because she was jeopardizing the health of the American people. And her policies were the policies of the Reagan administration, not Anne Burford."

Ruckelshaus has indicated he hopes to forge a middle road between the positions of his predecessors and those of environmentalists, to find politically acceptable ways to cut the regulation of business without triggering accusations that public health is being compromised.

"If the American people want to see the onus of regulation lessened, we need to find ways to carry out our mission in a responsive way--more efficient, more self-executing [for business], less costly, less confrontational," Ruckelshaus said in a policy address last week. "In short, not how do we eliminate regulation but how do we rationalize it?"

This is essentially the agenda the Reagan administration has talked of for the last two years. But it is unclear whether it can be accomplished in the current political atmosphere. Investigations by six congressional panels have disclosed evidence of extensive industry influence over EPA decisions to relax regulations on polluters and on the manufacturers of toxic chemicals.

The FBI is also investigating charges that agency officials had illegal conflicts of interest with companies they were supposed to regulate, and that their decisions were motivated more by a desire to assist Republican politicians than to protect public health.

Public opinion polls show more than 90 percent of Americans oppose efforts to relax the Clean Air and the Clean Water acts. A recent poll showed that Americans believed 2 to 1 that Reagan is more interested in helping business than in enforcing environmental laws.

Ruckelshaus indicated that these impressions pose a hindrance to administration efforts to cut regulations on business, and that he believes they can be changed.

"Public trust will only come if the public believes we are doing our very best," Ruckelshaus said. "That trust is sacred between us and the public and it must never be broken."

Since Reagan took office, the EPA's budget for every environmental protection program has been reduced, and congressional analysts report that the agency's overall spending power has dropped 50 percent. In the last year of the Carter administration, the EPA's operating budget was $1.35 billion, compared with Reagan's proposal of $949 million for the next fiscal year.

State pollution control programs have experienced some of the largest cutbacks in federal aid, although the administration has vastly increased state responsibility for preventing air, water and toxic pollution. State officials said they cannot maintain current levels of air and water quality unless budgets are increased.

Congressional critics point out that budget policy was set not by Burford but by Office of Management and Budget Director David A. Stockman. Although Ruckelshaus has been promised more latitude in the EPA than Burford, it is not clear whether he will be able to override Stockman.

The backlog of EPA regulatory actions, always large, has grown in the last two years, according to agency officials. The Natural Resources Defense Council recently estimated that 90 percent of all regulatory actions, from monitoring to enforcement efforts, are behind schedule, suspended or postponed.

The Reagan administration, in a major policy change from its predecessors, requires all new regulations to undergo a rigorous review by OMB analysts. Environmentalists have argued that this process effectively has blocked or postponed regulations on business, with officials arguing that proposed rules would cost industry more than they would benefit society. Several congressmen have contended that it is contrary to environmental law to put a dollar value on protecting public health.

The EPA's hazardous waste cleanup program, whose tattered record set off the national controversy over the agency, needs infusions of money, manpower and credibility, according to EPA officials and congressmen. The EPA has identified 419 hazardous waste sites across the country that pose the most imminent danger to public health, and EPA officials have said thousands more urgently need attention.

In the last two years, the EPA has cleaned up five of those sites under the $1.6 billion "Superfund" program, created by Congress to pay for removing toxic contamination and prosecuting companies responsible for it. Congressional critics in both parties have said EPA officials spent more time gathering scientific data on dangers posed by the sites than on determining how to clean them up. Rita M. Lavelle, ousted chief of the hazardous waste cleanup program, recruited industry-oriented science advisers whose studies often played down threats of chemical contamination, according to several of her former aides.

Ruckelshaus will be faced with a major policy debate on how the EPA should enforce laws against polluters. One of the key issues in the EPA controversy has been an agency policy of attempting to settle cases against polluters through out-of-court negotiations, rather than through litigation.

Many environmentalists also have said that the EPA cannot afford to take every case to court. But congressional critics have charged that this policy in the last two years resulted in "sweetheart deals" with polluters, allowing them to pay minimal fines for contaminating the air, water or land. In the Superfund program, several agency officials contended that this approach left the EPA without the resources to finance full cleanups.

Congressmen investigating the agency have been critical especially of EPA's failure to utilize a provision in the Superfund law that allows the government to use its resources to clean up toxic dumps, and then collect triple damages from responsible companies through litigation.

The budget for studying the environmental and health effects of chemicals and of all forms of pollution has been more than halved since Reagan took office. EPA's proposed budget for next year would reduce it to 45 percent of the money spent on research and development in the last year of the Carter administration.

The agency uses research data to determine whether to tighten or relax pollution regulations and also to assess the environmental impact of regulatory changes. Scientists have criticized cutbacks in research as a deterrent to effective regulation. They have also called for more research money to assess the health and environmental impacts of administration moves to relax regulations on business.

Both environmentalists and industry groups are watching closely to see whether Ruckelshaus will continue the administration drive to relax portions of the major laws enforced by the EPA. The Clean Air Act, the Clean Water Act, the federal pesticides act and the federal law regulating hazardous waste disposal are on the agenda of the 98th Congress for reauthorization.

Proposals by industry groups and the White House to relax portions of these laws died in the 97th Congress as did environmentalists' efforts to strengthen the Clean Air Act, adding controls on sulfur dioxide emissions that contribute to acid rain.