This paper examines risk factors that exist in the lives of incarcerated parents and their children, focusing on the living arrangements of the children. It uses data from the 1997 Survey of Inmates in State and Federal Correctional Facilities to address three issues: risk factors present in the lives of incarcerated parents and their children, how children in some living arrangements might be more vulnerable than others, and whether these risk factors predict where a child is placed during the parent's incarceration. The paper begins by reviewing the literature on the effects of parental incarceration on children, then discusses how substitute care arrangements relate to child outcomes. Study results indicate that there are many risk factors in the lives of incarcerated parents and their children. Children are increasingly likely to be placed with someone other than a parent, and are particularly likely to be placed in foster or agency care, as the number of risk factors rises. For both mothers and fathers, four risk factors significantly relate to child placement in foster care or an agency (history of physical or sexual abuse, less than a 12th grade education, and welfare benefit receipt). History of mental health problems is not a significant factor. Some gender and racial differences are present. (Contains 92 references and 6 tables.) (SM)