Facing criticism at home and calls to raise rights issues with Saudi leaders, May insisted she had no problem talking about "hard issues" on foreign visits.
But, less than a week after Britain officially started a two-year countdown for quitting the European Union, May made clear that economic issues were the priority.
May began a three-day Middle East tour on Monday in Amman, where she touted cooperation between British forces and Jordan's military in the fight against the Islamic State jihadist group.
Both countries are part of the US-led coalition that has been carrying out air strikes and supporting local forces against IS in Syria and Iraq since mid-2014.
Official news agency Petra reported Tuesday that May had departed for Riyadh, where she was to have two days of talks with senior officials including King Salman and the country's powerful two crown princes.
In a statement ahead of the visit, May said she would be looking to use the "immense potential for Saudi investment to provide a boost to the British economy".
Britain is looking to strike new trade deals as it prepares to leave the EU, with a major focus on longtime partners like the energy-rich Gulf states.
Qatar, for example, announced plans last month to inves 5 billion pounds ($6.23 billion/5.8 billion euros) in Britain within five years.
Saudi Arabia is Britain's largest trading partner in the Middle East, with exports of more than £6.5 billion in British goods and services to the country in 2015.
Saudi Arabia is also looking at boosting its foreign investments as part of a long-term plan known as "Vision 2030" to diversify its economy and reduce its dependence on oil revenues.
May came under fire ahead the visit, with opposition Labour Party leader Jeremy Corbyn demanding she raise concerns about "the dictatorial Saudi monarchy's shocking human rights record".
Call to halt arms sales
He called on Britain to halt arms sales to Riyadh immediately and to push for a ceasefire in Yemen, where a Saudi-led coalition intervened two years ago.
The coalition has carried out hundreds of air strikes and sent troops to support Yemen's internationally recognised government against Iran-backed Shiite Huthi rebels who have seized control of large parts of the country.
More than 7,700 civilians have been killed and a further 42,500 wounded since the start of the campaign, according to the United Nations. Seven million Yemenis are also facing starvation.
Rights groups including Amnesty International and Human Rights Watch have been among organisations calling for an end to arms sales from Britain and the United States to Saudi Arabia over the coalition's actions in Yemen.
On Sunday, Britain apologised after an egg was thrown at Saudi General Ahmed Assiri, the spokesman for the coalition, during a recent visit to London.
An anti-war activist last week attempted a citizen's arrest of Assiri, before another threw an egg that hit the spokesman in the back.
Asked by British reporters if she would bring up humanitarian and rights questions in Riyadh, May told Sky News: "We have no difficulty in raising hard issues with those that we meet, be it in Saudi Arabia or elsewhere in the world."
May also pointed to social reforms announced in the Vision 2030 programme, including plans to increase women's participation in the workforce from 22 to 28 percent by 2020.
Saudi Arabia has some of the world's tightest restrictions on women, and is the only country where they are not allowed to drive.
"I hope also that people see me as a woman leader, will see what women can achieve and how women can be in significant positions," May told the BBC.
May is also due to meet Sarah al-Suhaimi, who was appointed as the first female chair of the Saudi stock exchange earlier this year, and a Saudi princess appointed last year to oversee women's sports.
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