A two-day strike by healthcare assistants at three hospitals in West Sussex and Surrey started on Tuesday morning.
The Trust is urging the local community to choose services wisely to help ensure care is available for patients who need it most during the latest round of industrial action.
Nursing assistants and maternity support workers, who are members of union UNISON, are expected to take part in industrial action, today and 10 July.
The Trust said: "During previous actions, hundreds of patients still attended East Surrey Hospital’s emergency department.
"It is therefore vital that people who need care choose services wisely and consider if an urgent treatment centre or minor injury unit can help, find out more here. This will help ensure care is available to patients who need it."
This includes using NHS 111, walk-in-centres, GP practices, pharmacies, Crawley Urgent Treatment Centre and the Minor Injury Units at Caterham Dene, Horsham and East Grinstead for non-life-threatening care, and only using 999 or East Surrey emergency department in a genuine emergency.
They said that hospital staff will be working round the clock to ensure the safe care of all patients who need urgent and emergency treatment, as well as maintaining as much routine care as possible, and while disruption should be expected, the Trust are working hard to minimise this. People should therefore not put off seeking vital care on strike days.
Tina Hetherington, chief nurse at Surrey and Sussex Healthcare NHS Trust said: “While we are working round the clock to minimise disruption and care for all those who need us throughout this period of localised industrial action - our services are likely to be very busy.
“If your condition isn’t life-threatening, please do not attend the Emergency Department, and instead use other NHS services such as 111 online, your local pharmacy or GP, or nearby treatment centres at Crawley, Caterham Dene, Horsham and East Grinstead, which will be running as normal and will be able to see you much sooner. This will help ensure care is available to patients who need it most."