The contractor has offered workers in its timber division a 2.5% pay rise which has been turned down by GMB union members.
A ballot on possible strike action started on Monday and will close on February 17.
David Wood, managing director of Thomas Armstrong (Timber), told the Times and Star: “We feel we are making them a very good offer.
“Lots of companies are offering nothing and some are asking for wage reductions.
“Our major industries are in construction and furniture manufacture which are two of the worst hit, and we are supporting them at this time.
“We want to maintain these levels and keep them in employment.
“The workers got an increase last year and any increase this year will be backdated to the beginning of January, which has always been the agreement.
“It is a two-way thing. We have not been very busy and have had to move people around to maintain jobs.”
Kevin Young, GMB regional organiser, said: “GMB members in the company fully appreciate that these are very difficult times for everyone and they realise that it is a very challenging trading environment.
“GMB members employed within the timber department which makes pallets, roof trusses and drawer wraps and fronts are on wages marginally above the minimum wage and have not enjoyed a decent wage increase for a while.”
About 50 people work in the timber division, and Young said 60% were GMB members.