The CWU says BT can afford a 5% pay rise after what it says is a two-year wage freeze and round of redundancies.
The firm has offered a 5.1% rise over 21 months and several one-off payments.
The ballot closes after the delivery of first post on Monday and a result is expected later in the day. The earliest date a strike could be held is Monday 12 July.
As we reported a few weeks ago, the firm has been asking managers to provide details of their broader skills in case strikes go ahead to ensure that its 20 million business and residential customers, who have more than 30 million fixed voice lines and use the company as their provider of broadband services are as unaffected as possible should the strike go ahead.
The CWU says BT can well afford the pay increase after making profits of more than £1bn.
The union has previously warned BT that any legal challenge to the ballot, which BA had done in their ongoing battle with the Unite union, would not solve the dispute and only worsen the “already deteriorating” industrial relations.
BT had earlier said it was disappointed that the ballot was going ahead.
It also said last month that it had improved its offer several times, but that there had been no corresponding movement in the union position.