Shell is to outsource more than 3,000 IT jobs worldwide to AT$T, EDS and T-systems as part of a plan to save £250m a year.
The move will affect about 300 people working in Shell's IT operations in the UK.
Those affected are unhappy about being offered lower redundancy packages than other categories of employees.
Shell is offering packages worth only £50,000 to IT staff instead of the standard £200,000 packages.
The lower packages were introduced in June last year, when Shell said the £200,000 packages were only for employees who worked offshore on oil rigs.
Amicus said the larger packages were negotiated by a committee that included onshore workers and therefore should apply to everyone, including IT staff.
The decision to outsource the company's IT infrastructure came as a result of a review in 2005. The outsourcing deals are expected to be finalised by mid-2008.