[en] The ring injection and extraction systems must function as designed in order for the Spallation Neutron Source (SNS) to achieve its specified performance. In commissioning and early operations we have encountered problems that have been traced to these systems. We experienced high beam losses in and around the injection dump, the rectification of which has necessitated ongoing study and development by a multidisciplinary team. Results already include a number of enhancements of existing features and the addition of new elements and diagnostics. The problem in the extraction region stems from tilted beam distributions observed in the ring-to-target beam transport line (RTBT) and on the target, thus complicating the control of the beam-on-target distribution. This indicates the inadvertent introduction of x-y beam coupling somewhere upstream of the RTBT. The present paper describes computational studies, using the ORBIT Code, addressed at the detailed understanding and solution of these problems.