Boston's newest and most expensive landmark, the ill-fated John Hancock building in Copley Square, may soon reach the end of its ordeal.

The John Hancock Mutual Life Insurance Company announced earlier this week that it plans to replace the building's 10,348 double-paned windows with high-strength half-inch thick monolithic glass.

The windows, which cost $700 each, have been falling out since they were installed in the summer of 1972, reportedly due to high winds and settling in Copley Square's soft ground.

The problem has puzzled engineering specialists at MIT and Hansen, Holley and Biggs, a consulting firm in Cambridge called in in January to isolate the cause of the breakage.

The mottled 60-story tower dominates the Boston skyline with over 3500 panes now replaced by plywood.

The estimated cost for replacing the original windows is $5 to $7 million, according to Glenn H. Parsons, second vice-president of public relations for Hancock. The issue of who will finally foot the bill is still unresolved, and company officials have advised the people involved to refrain from comment on the matter.

The plague-ridden Hancock Company was confronted with heated objections from neighbors and architects when it announced plans for the construction of the tower in 1967.

The company is currently being sued by the City of Boston and three utility companies for $4 million in damages to sewage and water mains and communications lines allegedly caused by the construction of the skyscraper.

Historic Trinity Church, now dwarfed by the highest building in New England, has received extensive damages due to the flow of mud beneath its wooden foundations. The Hancock Company has agreed to pay for repairs.

Boston police closed off neighboring streets to traffic because of falling glass on several occasions during this year and an enclosed walk now surrounds the building to protect pedestrians.

Workmen will meticulously knock out each of the building's 55-square-foot windows, as the entire pane cannot be removed in one piece. The total cost for installing the first set of windows was $6.9 million.

The original insulating glass was from one-fourth inch to 5/16 inch wide, with a one half inch space between the panes.

The 16 acres of new glass will retain the unique reflective quality of the original glass, which was designed to mirror the clouds.

The new glass, specially designed to withstand high winds at various points outside the building, is scheduled to undergo some further testing before installation.

The original date for occupancy by the Hancock Company and three leasers was February 1973. The replacing of the windows with the special glass, which was recommended by architects I.M. Pei and Partners, a glass manufacturer and structural steel firm, is expected to begin shortly.

Barring any further mishaps, the skyscraper should be ready for occupancy by September 1974.

Until then the browsers and shoppers in Copley Square can gaze on the craftsmanship of Henry Hobson Richardson's Trinity Church, dnagle their feet in the fountain beside the church, or stroll through the new wind of the Boston Public Library.

But they had best not gaze up the 60 stories of the Hancock Building unless they prepare themselves for an aesthetic shock. For hovering above Copley Square--one of Boston's most pleasant sections--is the unfinished checkered Hancock monolith.