The investigators are performing a gene therapy clinical trial in Becker muscular dystrophy (BMD) and sporadic inclusion body myositis (sIBM) patients. Both of these conditions have an important common feature: loss of ability to walk because of weakness of the thigh muscles. The investigators plan to do a gene therapy trial to deliver a gene to muscle called follistatin (FS344) that can build muscle size and strength. If successful, the investigators can increase the size of the thigh muscle and potentially prolong a patient's ability to walk. The gene will be carried into the muscle by a virus called adeno-associated virus (AAV). This virus occurs naturally in muscle and does not cause any human disease, setting the stage for its safe use in a clinical trial. Presently there is no treatment that can reverse Becker muscular dystrophy or sporadic inclusion body myositis. Only supportive care is currently possible. In this study, subjects with either of these diseases will have shots of the follistatin gene injected directly into thigh muscle on one (first cohort) or both legs (2nd and 3rd cohort). One hundred and eighty days following the gene delivery, the muscle will undergo biopsy to look closely at the muscle to see if the muscle fibers are bigger. Between the time of the gene transfer and the muscle biopsy, patients will be carefully monitored for any side effects of the treatment. This will include an MRI of the thigh muscle before treatment and at day 180 following treatment. Blood and urine tests, as well as physical examination will be done on the subjects during the screening visit and on days 0, 1, 2, 7, 14, 30, 60, 90, and 180 to make sure that there are no side effects from the gene injections. Sutures will be removed 2 weeks post-biopsy. Additional blood samples will be collected at 9, 12, 18, and 24 months. Patients will be seen at the end of 1st and 2nd years for a physical exam, assessment of muscle strength and appropriate blood tests.