The Hammers have just eight points from 13 away games all season and have lost their last five away matches in the Barclays Premier League.
Assistant manager Neil McDonald hopes United, who last picked up a point on the road in the December draw at West Brom and most recently claimed three in the win at Newcastle in mid-November, can improve their record of three wins in 18 matches tomorrow and draw level on points with opponents Stoke.
"It's a stern test," said McDonald, who assumed manager Sam Allardyce's pre-match media duties.
"I think they're very well organised. They're quite direct with the way they play, into the forwards, then knocking it down and getting it wide.
"We have to deal with crosses, we have to deal with knock downs as well.
"Hopefully with our game and our game plan we can give them a little bit of a test as well.
"We're looking forward to the game and we're trying to put right what we haven't done over the last four or five away games."
Stoke have one win in five matches and McDonald hopes the Hammers can extend the hosts' poor run, having pushed high-flying Tottenham close on Monday night only for Gareth Bale to score twice to seal a 3-2 victory for his side at Upton Park.
McDonald added: "You always have to take something positive. Apart from Gareth Bale on Monday scoring two goals we've acquitted ourselves really well against a top-four team.
"If we do that away from home, we've got every chance of getting a result."
McDonald is trying to focus on the positives with his side's safety still to be assured.
The 14th-placed Hammers have 30 points and sit six points above the relegation zone.
They will have to perform without captain Kevin Nolan, at least in the short term, after the midfielder was ruled out with a broken toe.
Reports had suggested Nolan could miss up to eight weeks and therefore a significant portion of the season run-in.
West Ham hope intensive treatment will allow Nolan to return for the next league fixture, on March 17 at Chelsea.
Mark Noble is doubtful with an arm problem, but Guy Demel is fit to continue despite going off against Spurs.
Demel was replaced by Emanuel Pogatetz, who was given a torrid time by Aaron Lennon, but has been backed by McDonald.
McDonald said: "He was against a good player in (Aaron) Lennon. He had a few problems; he didn't stop enough crosses.
"It's always difficult in the last 20 minutes coming into a game.
"He's settled in okay."