New regulations limiting eligibility for the Aid to Families with Dependent Children program will knock 4,000 families off welfare in the Washington area, according to officials in the District and nearby counties. There are about 13,000 individuals in these families.

Washington itself is by far the hardest hit and will have to drop about 2,500 cases. Originally, the city was to drop as many as 3,500 families, but the District voted overwhelmingly to offset the Reagan cuts with funds from city coffers. City officials also are waiting until Jan. 1 to implement the changes, in part because the city does not want to spoil anyone's Christmas.

Maryland moved quickly to adopt the new regulations Oct. 1, though a lawsuit in Baltimore postponed implementation for a month. Prince George's County dropped 900 cases; Montgomery lost about 400. Some of the Maryland families may be put back on welfare rolls, however, if the state legislature approves a plan that would use state funds to help pay for extra benefits.

Arlington, Fairfax and Alexandria, with smaller welfare rolls, lost fewer cases. The numbers -- still estimates -- are 90 in Arlington, 88 in Alexandria and 120 in Fairfax. Virginia cuts took effect in November.

An unidentifiable number of additional welfare families will have their benefits reduced under the new regulations. And on Feb. 1, under the new rules, those few working poor who have remained on AFDC could be dropped from the rolls. On that date, recipients of AFDC who work will no longer be able to "disregard" $30 a month plus one third of their income -- the last existing work incentive in the system.

Nationwide the government estimates that 687,000 of the 3.9 million families receiving public assistance will be dropped or have their benefits cut when the new rules are fully operational.

The cuts imposed by Congress at President Reagan's request will operate differently in different states, depending on local welfare law. The states share any savings from the changes with the federal government, since AFDC financing is shared between the federal and state governments. President Reagan has said that the federal Treasury will save $7 billion during the next five years because of the new regulations.

Those rules affect AFDC recipients in three basic ways. They make it much more difficult for anyone with a job to stay on welfare by establishing that anyone earning at least 150 percent of the local welfare "standard of need" for families of the same size is automatically ineligible for any AFDC assistance. This means that most families that include anyone with a full-time job, even for the minimum wage, are ineligible for AFDC.

Previously the program included a deliberate work incentive that allowed people to deduct some of their earnings and expenses associated with their jobs before their eligibility was calculated. This allowed working mothers, for example, to hold down minimum-wage or even better-paying jobs while still receiving welfare, food stamps and Medicaid for health care. Under the new rules, much smaller deductions for day care and work expenses are allowed, but only after a would-be client qualifies under the strict income limits.

Second, the new rules require that a man married to an AFDC recipient, but not the father of her children, must report his income to the welfare authorities and, in many cases, allocate a portion of it to maintenance of the household. Previously, a stepfather's income had no bearing on a mother's eligibility for AFDC.

Under the new rules, either the head-of-household's earned income or a stepparent's income can be used to justify dropping a welfare client altogether or reducing the client's benefit check.

The third major consequence of the new rules, according to local welfare officials, is a provision denying payments to women who are pregnant for the first time until the third trimester of their pregnancy. In Maryland, for example, under the old rules a pregnant woman could apply for aid for herself and for her expected child as soon as her pregnancy was confirmed. In other words, the pregnant woman qualified as a two-member household. Now, only the baby qualifies for AFDC aid, and not until the third trimester of pregnancy.

Montgomery County and the District will soften the impact of these changes somewhat. Washington will continue aid to pregnant women and pick up the full cost out of city revenues. Montgomery gives a supplemental grant of at least $33.50 a month to recipients, and will continue to do so. Montgomery also hopes to put some who have lost their benefits onto county medical assistance. In other jurisdictions, loss of AFDC benefits means loss of Medicaid, as well, in most cases.

Medical care is an example of the ambiguities created by these cuts. In Prince George's County, the public hospital is obliged by law to give care to any resident who appears at its doors. A source familiar with the workings of the hospital said that if a patient, deprived of a Medicaid care because of the new AFDC cuts, came for serious medical treatment, the hospital would be tempted to keep that patient long enough to run up a large bill. With such a bill owed, the patient might again become eligible for Medicaid benefits.

In some other respects the new cuts will turn out to be something other than Congress and the White House have advertised. For example, the administration got a lot of publicity by proposing that states deny welfare to anyone with personal property or financial assets worth more than $1,000. Local jurisdictions say they have no intention of attempting to do this, primarily because they believe it would cost more to administer the idea than enforcing it could possibly save.