The stock market appeared to explode in joy yesterday in celebration of Ronald Reagan's landslide presidential victory and the unexpected Republican takeover of the Senate for the first time in a quarter of a century.

The Dow Jones industrial average soared nearly 30 points in the first few hours of trading with heavy buying reported in defense and oil stocks. The Dow was up 15.96 points at the close in the heaviest trading day in Wall Street history.

Adding to the business euphoria were reports from Reagan's economic advisers that the president-elect would push quickly for large tax cuts tied to budget measures aimed at slowing the growth in federal spending.

General Electric Chairman Reginald Jones called the election a "watershed." He expressed both the hope and the belief that the Reagan administration would have the political courage to attack inflation while providing new incentives for savings and investment -- a sentiment that has echoed throughout the business community during a long election campaign.

A survey of Reagan's key economic advisers yesterday indicated the new administration probably would stick to its pledge to seek a 10 percent across-the-board cut in personal taxes next year. Casper Weinberger, a former budget director in the Nixon administration and now a Regan adviser said he saw little flexibility in the new administration's commitment to the tax-cut plan. This, basically, is the first installment of the Kemp-Roth tax plan now before Congress.

Business leaders surveyed by The Washington Post yesterday saw the election as a chance to "rationalize" rather than repeal what they saw as out-of-control federal regulations in such areas as the environment and safety on the job.

The biggest change for the business community, however, was in the Senate were conservative Republicans are positioned to take over the chairmanships of almost every major committe involved with business legislation.

Such familiar names to the business community as Russell Long, William Proxmire and Edward Kennedy will give way in January to names such as Robert Dole, Jake Garn and Strom Thurmond.

Dole, a Kansas Republican, is expected to replace Long as chairman of the Senate Finance Committee while Garn of Utah probably will replace Proxmire as chairman of the Senate Banking Committee. South Carolina's Thurmond is slated to replace Kennedy as chairman of the Senate Judiciary Committee with its oversight of federal antitrust laws.

Key committees where business has never dealt with anyone but a Democratic chairman include Energy, where Sen. Henry Jackson (D-Wash.) is expected to be replaced by Sen. James A. McClure (R-Idaho), and Commerce, where veteran Sen. Howard Cannon (D-Nev.) will most likely be replaced by Sen. Robert Packwood (R-Ore.).

The biggest changes are expected to occur in the banking and energy areas where Garn and McClure are expected to produce a fundamental shift in the direction of their committees.

Garn, unlike Proxmire who saw himself as a champion of the consumer, is expected to be much more pro-banking.

And the rise of McClure to the Energy Committee chairmanship is expected to enhance Reagan's chances of further decontrolling the nation's energy industry.