More than 500 parents and scouting officials from around the country, concerned about reports of toxic dioxin-contaminated soil at the site of the Boy Scout 1981 jamboree at Fort A.P. Hill in Virginia, telephoned the organization's headquarters in Irving, Tex., yesterday, according to a Scout spokesman.

Testing by a private engineering firm will begin today at the site, which also is scheduled to host next summer's jamboree, and the spokesman said results are expected by the end of this week.

Scouting officials say that the contamination level was too low to pose a health threat either in 1981 or now.

The spokesman said that most callers wanted to know whether boys who attended the 1981 jamboree should be examined by a doctor, of if any health hazard exists for the next jamboree. The spokesman said the Boy Scouts would withhold any further statement until the test results are available.

About 31,000 scouts attended the 1981 jamboree, and another 28,700 are expected in July 1985 for the 11th National Boy Scout Jamboree.

Army officials have said that the military would "move aggressively" to dismantle a small shed, identified as a possible source of contamination because it had been used until 1978 as a storage place for liquid herbicides. The corrective work will include cleansing of the area surrounding the shed of any residue of the herbicides before the scheduled arrival of the scouts, officials said.