Graeme McCallum, 49, head of McAlpine's housing division, and Eric Grove, 66, a non-executive director, were detained following an investigation by the Inland Revenue. Derek Green, a consultant employed by the stockbroker Gerrard Vivian Gray, with no apparent links to McAlpine, was also arrested after tax officials visited several premises.
Alfred McAlpine said it had been informed that two of its offices had been visited by the Inland Revenue.
"The board has been assured by the Inland Revenue that the reason for this visit is not in any way related to the business or tax position of Alfred McAlpine or any of its subsidiaries but relates to the personal affairs of Mr Grove ... and Mr McCallum."
The Inland Revenue declined to give further details about the investigation because it was still continuing.
However, it is understood that the false accounting charges may be linked to recent earn-out payments arising from McAlpine's acquisition in 1988 of Solihull-based Canberra, a privately-owned housebuilder controlled by Mr Grove.
Mr McCallum was Canberra's managing director at the time of the merger.
Under the terms of the deal, McAlpine took a 60 per cent stake in Canberra for an undisclosed sum. Mr Grove, his wife, son and daughter received a total of pounds 3m in special dividends in each of the two following years.
In 1992, Mr Grove agreed to sell his remaining 40 per cent interest in Canberra to McAlpine for pounds 8.4m in cash and shares with a future earnings- related payment of at least pounds 9m to come.
According to McAlpine's latest set of report and accounts, the total deferred consideration for Canberra - since renamed Alfred McAlpine Developments Ltd. - is payable this year.
In a note to the accounts, McAlpine says the sum "is not expected to differ significantly from the amount included in the balance sheet as at 31 December 1994 of pounds 15.3m."
Mr Grove was appointed to the McAlpine board in 1990 and sits on its audit and remuneration committee. Mr McCallum joined McAlpine in 1988 following the merger with Canberra, where he was managing director. He was previously with Barratt Developments.
The arrests of two senior executives are yet another embarrassment for McAlpine, which last month reported a pounds 23m loss for 1995 following the closure of its loss-making building division. Last September a leaked letter from Hambros' deputy chairman, Sir Chips Keswick, acting on behalf of the McAlpine family trusts that own 15 per cent of the company, accused the construction group of poor management and urged it to sell out to a larger rival.
Shares in McAlpine fell 7p to 180p on news of the arrests.