Revd Yat Michael and Revd Peter Reith, from the Presbyterian Evangelical Church, have been accused of undermining the constitutional system of the Sudanese Penal Code; waging war against the state; disclosure and receipt of official information or documents; arousing feelings of discontent among regular forces; breach of public peace; and offences relating to insulting religious beliefs.
Their families were refused access to the Omdurman Men's Prison in June, a low security facility, where they had been since March.
Prison authorities have now confirmed the pastors had been transferred to Kober Prison in the capital, Khartoum.
It has been reported that neither their wives nor lawyers have been allowed to visit them and no reason for the move has been released.
Christian Solidarity Worldwide's Chief Executive Mervyn Thomas said: "We are concerned by this development in the clergymen's case.
"They already endured extended detention without access to their families at the beginning of this year and they and their families should be spared further emotional distress.
"Moreover, the refusal of access to their legal representatives is in violation of article 14 of the International Covenant on Civil and Political Rights (ICCPR), to which Sudan is party, and which guarantees the right of those charged with a crime to communicate with counsel of their own choosing.
"We urge the Sudanese authorities to ensure that the clergymen's detention is regularised, and they are permitted regular family visits and unhindered access to their lawyers.
"The decision to detain them at a higher security prison should be reconsidered, given that they have not been found guilty of any crime."