HP workers at the Department of Work and Pensions (DWP), the MoD and General Motors will be on strike for four more days in two 48 hour stoppages.
The workers, which are members of the Public and Commercial Services union (PCS), are based in the north east and north west of England.
Up to 1,000 staff, which have already been on strike for a total of three days, will walk out on the 29 and 30 March as well as 6 and 7 April.
The union is in dispute over fair pay and job security. Many of the workers are former staff of EDS which was acquired by HP in 2008.
Mark Serwotka, PCS general secretary, said: "Staff have worked hard to help the company deliver billions of pounds in revenues and feel betrayed by HP's refusal to address concerns on jobs and pay.
"The escalation of their campaign illustrates the determination of HP staff to achieve guarantees on job security and a fair pay rise. the company needs to start valuing its own workforce and negotiate a settlement that addresses the concerns of the workforce."
The union will also be launching a petition and seeking the support of MPS.