The team managed to convert ordinary skin and bone tissue cells from patients with these diseases into stem cells which contain the same genetic fault.
This could help step up research into finding an eventual cure, the study said in the latest edition of Cell magazine.
"Researchers have long wanted to find a way to move a patient's disease into the test tube, to develop cells that could be cultured into the many tissues relevant to diseases of the blood, the brain and the heart, for example," said investigator George Daley.
"Now, we have a way to do just that, to derive pluripotent cells from patients with disease, which means the cells can make any tissue and can grow forever.
"This enables us to model thousands of conditions using classical cell culture techniques."
Daley, from Children's Hospital Boston, worked with researchers from Harvard Medical School, Massachusetts General Hospital, and the University of Washington to create the disease-specific stem cell strains.
Such cells reproduce human illnesses more faithfully than those taken from animals such as mice.
Although the genetic differences between the two are small in some diseases, such as Down's Syndrome, the genetic fault does not trigger the same reaction in mice as in humans.
Other diseases which may be more closely studied thanks to this technique include juvenile onset diabetes; Huntington's disease; Down's syndrome and ADA-severe combined immunodeficiency, a form of the disorder commonly known as "boy-in-the-bubble disease."