Информация с минского сайта посольства США в Беларуси: http://minsk.usembassy.gov/general_information.html
Emergency Visa Appointments
There are several sets of circumstances in which a visa to travel to the United States becomes an emergency: visas for medical treatment, emergent business, death in the family, etc. If you feel that you have a legitimate need to request an Emergency Visa Appointment, please contact the Consular Section at +375-17-210-1283. Requests will be considered on a case-by-case basis. Please be prepared to provide specific information regarding your emergency.
Please note that applicants using an Emergency Visa Appointment are subject to all nonimmigrant visa requirements and procedures as listed on the Nonimmigrant Visas page and does not guarantee visa issuance. In addition, the issuance of a visa does not automatically guarantee entry to the United States; the Department of Homeland Security, US Customs and Border Protection officials at ports of entry have authority to admit or deny entry to the U.S.
If you feel that you have a legitimate need to request an Emergency Visa Appointment, please contact the Consular Section at +375-17-210-1283. Requests will be considered on a case-by-case basis.
The following fees are applicable to Belarusian citizens:
Single entry business/tourist/visitor visa - No fee ($100 application fee applies)
Multiple entry one-year business visa - US$ 100
Multiple entry one-year work visa - US$ 300
Transit visa - No fee
плюс, думаю, ещё надо [insurance] будет им покупать.